Foundations and Applications of Non-Equilibrium Statistical Mechanics

19 Sept 2011, 08:00 → 14 Oct 2011, 18:00 Europe/Stockholm

132:028 (Nordita)

Alberto Imparato (University of Aarhus), Carlos Mejía-Monasterio (University of Helsinki), Hans Fogedby (University of Aarhus), Ralf Eichhorn (Nordita)

A Nordita scientific program is an extended workshop where a limited number of scientists work together on specific topics for a period of several weeks. This program is centered around modern developments in non-equilibrium statistical mechanics both with respect to fundamental aspects (fluctuation theorems, entropy production, fluctuation-dissipation theorems) as well as applications (noise-induced phenomena, biophysical problems).

The program aims at but is not limited to the following topics:

The second law (extensions to non-equilibrium) Entropy production Non-equilibrium steady states Quantum work relations Reconstruction of free energy landscapes

Nonequilibrium transport Fluctuation induced phenomena Brownian motion and stochastic processes Response behavior to external perturbations

The main objective is to bring together leading experts with strong background in statistical physics for an extended period of time, and to create a lively and fruitful atmosphere of intensive research and mutual interactions between the participants.

Strong emphasis is on informal discussion and working group meetings. It is planned to have a limited number of introductory or review-like talks, maybe around one per day, that may serve as “condensation nuclei” for subsequent discussions and projects. In order to provide a certain level of structuring, we intend to choose “focus themes” for the four different weeks of the program, so that talks, discussions and meetings are primarily around that theme:

week 1	(Sep 19 - Sep 23)	fluctuation theorems
week 2	(Sep 26 - Sep 30)	transport phenomena
week 3	(Oct 3 - Oct 7)	exactly solvable models
week 4	(Oct 10 - Oct 14)	applications

Nordita provides a full-fledged working environment for program participants, including office space, internet access etc.

Confirmed participants:

Mikko Alava (Helsinki) Tobias Ambjörnsson (Lund) Erik Aurell (Stockholm) Felipe Barra (Santiago - Chile) Sergio Ciliberto (Lyon) David Dean (Toulouse) Bernard Derrida (Paris) Abhishek Dhar (Bangalore) Jean-Pierre Eckmann (Geneva) Andreas Engel (Oldenburg) Massimiliano Esposito (Brussels) Denis Evans (Canberra) Martin Evans (Edinburgh) Pierre Gaspard (Brussels) Giovanni Jona-Lasinio (Rome) Ryoichi Kawai (Birmingham) Anatoly Kolomeisky (Houston) Joachim Krug (Cologne) Antti Kupiainen (Helsinki) Jorge Kurchan (Paris) David Lacoste (Paris) Michael Lässig (Cologne) Vivien Lecomte (Paris) Raphael Lefevere (Paris) Stefano Lepri (Florence)

Michael A. Lomholt (Odense) Jani Lukkarinen (Helsinki) Christian Maes (Leuven) Bernhard Mehlig (Gothenburg) Ralf Metzler (Munich) Namiko Mitarai (Copenhagen) David Mukamel (Rehovot) Paolo Muratore-Ginanneschi (Helsinki) Gleb Oshanin (Paris) Luca Peliti (Naples) Tomaz Prosen (Ljubljana) Andrea Puglisi (Rome) Peter Reimann (Bielefeld) Felix Ritort (Barcelona) Lamberto Rondoni (Turin) Keiji Saito (Tokyo) Shin-ichi Sasa (Tokyo) Udo Seifert (Stuttgart) Ken Sekimoto (Paris) Herbert Spohn (Munich) Peter Talkner (Augsburg) Christophe Texier (Paris) Mats Wallin (Stockholm) Frederic van Wijland (Paris) Angelo Vulpiani (Rome)

Sponsored by:

Registration deadline: 25 July 2011

Monday, 19 September

09:00 → 10:00 Welcome breakfast & Registration

10:00 → 10:15 Welcome and Opening Remarks

10:15 → 11:00 Dissipation and the foundations of classical statistical mechanics

Over the last 15 years we have discovered a group of related theorems that enable us to prove the ”laws” of thermodynamics. Each of these ”laws” is provable for time reversible, deterministic equations of motion that satisfy a mathematical condition called T-mixing. The axiom of causality is also required. These proofs involve a new mathematical quantity first defined in 2000, namely dissipation. Dissipation, not entropy, turns out to be the central quantity for the fluctuation theorems, the dissipation theorems, linear and nonlinear response theory, and the relaxation theorem. Using dissipation, we can also derive Clausius’ Inequality and Equality, without assuming the Second ”Law” of thermodynamics.

Speaker: Prof. Denis Evans (The Australian National University, Canberra, Australia)

11:00 → 11:45 Quantum fluctuation theorems

The fluctuation theorems of Jarzynski and Crooks impose restrictions on the statistics of work performed by an external force acting on a system that initially was in thermal equilibrium. Originally these relations were proven for classical systems. In this talk we shall present how they can be obtained for quantum systems [1]. The first precondition for their validity is a proper and consistent definition for work performed on a quantum system. As a second condition the system must initially be prepared in a thermal equilibrium state and third, the dynamics must be microscopically reversible. We further shall discuss the validity of the fluctuation theorems for open quantum systems and for systems subjected to projective measurements. [1] M. Campisi, P. Hanggi, O. Talkner, Rev. Mod. Phys., 83, 771 (2011).

Speaker: Prof. Peter Talkner (University of Augsburg, Germany)

15:00 → 16:00 Coffee

Tuesday, 20 September

09:30 → 10:00 Coffee

10:00 → 10:45 Heat flux and the violation of Fluctuation Dissipation theorem during aging

Speaker: Prof. Sergio Ciliberto (Lyon)

10:45 → 11:30 The arrow of time in evolutionary biology

Evolution is a quest for innovation: organisms adapt to changing natural selection by evolving new phenotypes. At the molecular level, adaptive evolution takes place in a sea of stochasticity generated by random new mutations and fluctuations in reproduction. The irreversibility of adaptive evolution can be measured by a quantity called fitness flux. This talk addresses the statistical foundation of molecular evolution, which is provided by a fitness flux theorem. The theorem shows that evolutionary dynamics and modern nonequilibrium thermodynamics obey strikingly analogous statistical principles. We discuss how fitness flux can be measured, using genomic data of the human influenza virus.

Speaker: Prof. Michael Lässig (University of Cologne)

15:00 → 16:00 Coffee

Wednesday, 21 September

09:30 → 10:00 Coffee

10:00 → 10:45 Stochastic thermodynamics of non-equilibrium steady states: From the FDT to efficient nano-machines

Stochastic thermodynamics provides a framework for describing small systems embedded in a heat bath and externally driven to non-equilibrium [1]. Examples are colloidal particles in time-dependent optical traps, single biomolecules manipulated by optical tweezers or AFM tips, and motor proteins driven by ATP excess. For non-equilibrium steady states (NESSs), total entropy production obeys a detailed fluctuation theorem even for finite times [2]. As an alternative to the phenomenological approach of introducing an effective temperature in order to adjust the equilibrium form of the fluctuation-dissipation theorem (FDT) to a NESS, we have derived a transparent general form of the FDT in a NESS [3]. Moreover, generalized Green-Kubo relations hold true in NESSs under the weak assumption of local detailed balance [4]. Finally, this formalism allows to discuss the efficiency of autonomous soft nano-machines [5]. Where available, these theoretical results will be illustrated using data from experimental model systems. [1] U.S., Eur. Phys. J. B, 64, 423, 2008. [2] U.S., Phys. Rev. Lett. 95, 040602, 2005. [3] U.S. and T. Speck, EPL 89, 10007, 2010. [4] U.S., Phys. Rev. Lett. 104, 138101, 2010. [5] U.S., Phys. Rev. Lett. 106, 020601, 2011.

Speaker: Prof. Udo Seifert (Stuttgart University)

10:45 → 11:30 Field theoretic formulation of a mode coupling equation for colloids

Mode-coupling approximations are at the core of the analysis of the slow dynamical properties of glasses. Unfortunately, such approximations are neither controlled nor systematic. We propose a route to carry out such an approximation, based on field-theoretic techniques, that relies on a small parameter expansion and that can, in principle, be generalized to higher orders. Our approach is consistent with the fluctuation-dissipation theorem requirements.

Speaker: Prof. Frederic van Wijland (Laboratoire Matière et Systèmes Complexes, Université Paris Diderot)

15:00 → 16:00 Coffee

18:00 → 20:00 Conference dinner

Thursday, 22 September

09:30 → 10:00 Coffee

10:00 → 10:45 Current fluctuations in non-equilibrium systems

The talk will review a number of results obtained for diffusive systems on the fluctuations of the current of heat or of particles. It will also present more recent results on mechanical systems (hard particle gas) and on diffusive systems at a phase transition.

Speaker: Prof. Bernard Derrida (Laboratoire de Physique Statistique, Ecole Normale Supérieure, Paris)

10:45 → 11:30 Recent advances in free energy recovery of molecular structures

Speaker: Prof. Felix Ritort (Small Biosystems Lab, Universitat de Barcelona)

14:00 → 14:45 Equilibration and thermalization under realistic preparation and measurement conditions

Speaker: Prof. Peter Reimann (University of Bielefeld)

15:00 → 16:00 Coffee

Friday, 23 September

09:30 → 10:00 Coffee

10:00 → 10:45 Asymptotics of work distributions in Langevin systems

Non-equilibrium work and fluctuation theorems highlight the large-deviation properties of thermodynamic quantities. Accordingly the tails of the probability densities of work, heat, or entropy are of special importance. However, by their very definition rare realizations from these tails are difficult to observe in experiments or simulations and the resulting histograms are imprecise exactly in the region of highest interest. The situation may be improved by combining the histograms with analytical expressions for the asymptotics of the probability distributions. In the case of driven Langevin systems the asymptotic behaviour of the work distribution can be determined from a saddle-point approximation in the functional integral describing the transformation of probability from the trajectory to the work. The calculation of the pre-exponential factor may improve the accuracy of the method substantially and allows to combine histogram and asymptotics without adjustable parameters. For the special case of harmonic potentials with time-dependent frequency the asympotitics of the work distribution is always exponential.

Speaker: Prof. Andreas Engel (University of Oldenburg)

10:45 → 11:30 Physics and Information Theory: Landauer's principle and beyond

The Landauer's principle states that erasure of a bit of information requires at least k*ln2 of entropy production. This principle becomes a foundation of the relation between information theory and physics. Since its inception, the principle has been challenged by many people while others have demonstrated its validity. Due to the lack of rigorous proof, there have been many misleading statements about the principle. In fact, the above statement of the principle itself invites misinterpretation. The recent development in nonequilibrium statistical mechanics provides us with tools to investigate the relation between information and physics. Nevertheless, there are still misunderstanding and misleading statements in recent literature. In order to stimulate discussion at NORDITA, I will present a brief review on the issues related to the Landauer's principle and thermodynamics of logic gates utilizing the recent understanding of irreversible processes.

Speaker: Prof. Ryoichi Kawai (Department of Physics, University of Alabama at Birmingham)

15:00 → 18:00 Reception

Monday, 26 September

09:00 → 10:00 Welcome breakfast & Registration

10:00 → 10:45 An infinite set of Second Law-like inequalities

Speaker: Prof. Jorge Kurchan (École Supérieure de Physique et de Chimie Industrielles, Paris)

10:45 → 11:30 Initial growth of Boltzmann entropy and chaos in a large assembly of weakly interacting systems

Speaker: Prof. Lamberto Rondoni (Dipartimento di Matematica, Politecnico di Torino)

14:00 → 14:45 On anomalous diffusion and the out of equilibrium response function in one-dimensional models

We study how the Einstein relation between spontaneous fluctuations and the response to an external perturbation holds in the absence of currents, for the comb model and the elastic single-file, which are examples of systems with subdiffusive transport properties. The relevance of non-equilibrium conditions is investigated: when a stationary current (in the form of a drift or an energy flux) is present, the Einstein relation breaks down, as is known to happen in systems with standard diffusion. In the case of the comb model, a general relation, which has appeared in the recent literature, between the response function and an unperturbed suitable correlation function, allows us to explain the observed results. This suggests that a relevant ingredient in breaking the Einstein formula, for stationary regimes, is not the anomalous diffusion but the presence of currents driving the system out of equilibrium.

Speaker: Prof. Angelo Vulpiani (Dipartimento di Fisica, Università di Roma "La Sapienza")

15:00 → 16:00 Coffee

Tuesday, 27 September

09:30 → 10:00 Coffee

10:00 → 10:45 The motion of 1D driven interfaces: exact solutions of the KPZ equation

A widely studied nonequilibrium interface dynamics considers a stable phase in contact with a metastable phase. If the order parameter for the bulk phases is not conserved and mixes rapidly, the effective equation of motion for the interface was proposed by Kardar, Parisi, and Zhang some time ago. We explain some recent exact solutions of this equation in the case of a 1 D interface and their connection to the thin film turbulent liquid experiment by Takeuchi and Sano. In particular, the unanticipated role of replicas will be emphasized.

Speaker: Prof. Herbert Spohn (Zentrum Mathematik and Physik Department, TU M¨ unchen)

10:45 → 11:30 Nonequilibrium heat capacities

We define nonequilibrium heat capacities as the excess heat caused by variation of the environment temperature. The system itself is subject to nonconservative forces and maintains steady currents with corresponding dissipation (house-keeping heat). We show the correction to equilibrium expressions, how the heat capacity can get negative and we give some explicit examples. Joint work with E. Boksenbojm, K. Netočný and J. Pesek.

Speaker: Prof. Christian Maes (Instituut voor Theoretische Fysica, K.U.Leuven)

14:00 → 14:45 Mean first passage times: Meaningful or meaningless?

In many problems in physics, biophysics or chemistry one is often interested to know how fast a randomly moving ”particle” (a ligand, an ion, a protein, a reactant, a phage, etc) may find a particle of another species, a binding or a ”specific” site, an entrance/exit to a bounded domain, a receptor, a target, a source of odor, any ob ject in space, etc. A commonly used characteristic is the first moment of the first passage time distribution - the mean first passage time (MFPT), which in many cases can be evaluated or, at least, estimated analytically. The question is, however, how the MFPT is representative of an actual behavior. In the first, central part of this talk we overview some recent results [C. Mejia-Monasterio, G. Oshanin and G. Schehr, J. Stat. Mech. 2011 P06022 (2011)] for unbiased (centrally biased) Brownian search for an immobile target in bounded (or infinite) spherical domains. We use here a special novel ”diagnostic” of the first passage events: in our ”imaginary” experiment, instead of considering a single searcher, we launch simultaneously from the same point in space two absolutely identical non-interacting ones and calculate the distribution function P (ω) of a random variable ω = t1/(t1 + t2), where t1 and t2 are the (unordered) times of the first passage to the target for the searcher 1 and searcher 2, respectively. We show that P (ω) exhibits quite a non-trivial and sometimes a counterintuitive behaviour so that its very shape (a broad bell-shaped form with a maximum at ω = 1/2 or an M-like form with a minimum at ω = 1/2 and maxima close to 0 and 1) depends, remarkably, on the size of the system, the location of the starting point relative to the target and/or on the magnitude of the bias, if any. The shape of P (ω) appears also to be sensitive to the form of the domain: we demonstrate that for an infinite (finite) wedge or a 3D cone, or a triangle with adsorbing boundaries, the distribution P (ω) may have a bell-shaped or an M-like forms depending whether the value of the opening angle is less than or exceeds some critical value. Our results thus indicate that, despite the fact that the single-searcher first passage time distribution has moments of arbitrary order, the sample-to-sample fluctuations are very significant and the mean first passage time is not, in fact, a reliable measure of the first passage events. Further on, we will consider, within the framework of a model originally proposed by de Gennes [J. Stat. Phys. 12 463 (1975)], dynamics of a boundary separating the helix and coil phases in a partially melted heteropolymer bearing a random alphabet. For this model, a random variable ω is the alphabet-dependent probability that a randomly moving boundary will first hit the left extremity of the polymer (so that the chain will return to its native helix state) without having ever hit the right extremity, while t1 and t2 are the resistances of the two respective intervals to the left and to the right of the starting point. Hence, P (ω) is the probability distribution (averaged over all possible alphabets) of such a hitting probability. We show [G. Oshanin and S. Redner, EPL 85, 10008 (2009)] that also in this situation P(ω) exhibits a transition from a bell-shaped (for sufficiently short polymers) form to an M-like shape (for sufficiently long polymers). We therefore conclude that the evolution of a partially melted long random heteropolymer is controlled by the arrangement of monomers along the chain so that each heteropolymer realization has a unique kinetics and unique final fate that is not representative of the average behavior of an ensemble of such polymers. Finally, we will show that an analogous shape-reversal transition occurs in Black-Scholes model of stock options evolution. Considering two identical Black-Scholes stochastic equations, which produce two identical (uncorrelated or correlated) either European- or Asian-style options t1 and t2, we will demonstrate that the distribution function of the relative weight ω of either of the options in a portofolio composed of two such options undergoes at a certain moment of time a transition from a unimodal form with a maximum at ω = 1/2 to a bimodal form with a minimum at ω = 1/2, which reflects the symmetry breaking between two identical options [G. Oshanin and G. Schehr, Quantitative Finance, to appear; arXiv:1005.1760v2].

Speaker: Gleb Oshanin (Physique Theorique de la Matiere Condensee, Universite Pierre & Marie Curie, Paris)

15:00 → 16:00 Coffee

Wednesday, 28 September

09:30 → 10:00 Coffee

10:00 → 10:45 Thermodynamic formula for the cumulant generating function of time-averaged current

The main purpose of my talk is to present a new operational formulation for the cumulant generating function of time-averaged current. According to Einstein's fluctuation theory in equilibrium statistical mechanics, the cumulant generating function of extensive variable is related to a thermodynamic function,　 which leads to the fluctuation response-relation.　On the other hand, in non-equilibrium statistical mechanics, the fluctuation-dissipation theorem (FDT) for a current holds in the linear response regime, but the cumulant generating function of time-averaged current itself has never been considered in an operational manner like Einstein's　 fluctuation theory. Now, our formulation claims that the first derivative of the cumulant generating function is equal to the expectation value of the current in a modified system with an extra force added, where the modified system is characterized by a variational principle. The formula reminds us of Einstein's fluctuation theory and simultaneously it leads to the FDT when the linear response regime is focused on. In my talk, after quickly reviewing Einstein's fluctuation theory (in a little bit fresh form), I explain the main results of our formulation. Then, I　 mention similarities of our formulation with previously known theories such as　 the Donsker-Varadhan theory, the additivity principle, and the least dissipation principle. Finally, I discuss the range of the applicability of our formulation and some applications. This work was done in collaboration with Takahiro Nemoto. See arXiv:1109.

Speaker: Prof. Shin-ichi Sasa (The University of Tokio)

10:45 → 11:30 Microreversibility, current fluctuations, and nonlinear responses in nonequilibrium systems

The microreversibility of Newton's equations does not preclude that phase-space trajectories may be physically distinct from their time reversals. In statistical mechanics, a trajectory and its time reversal can thus have different probability weights, which breaks the time-reversal symmetry in the statistical description of nonequilibrium processes. This fundamental observation shows that microreversibility is compatible with the thermodynamic time asymmetry, allowing us to understand how directionality and dynamical order can be induced out of equilibrium. In this perspective, a fluctuation theorem for several coupled currents have been established thanks to network theory and new relationships between the fluctuation and response properties have been found, which are valid beyond the linear regime. References: • P. Gaspard, Time-Reversed Dynamical Entropy and Irreversibility in Markovian Random Processes, J. Stat. Phys. 117 (2004) 599-615. • D. Andrieux, P. Gaspard, S. Ciliberto, N. Garnier, S. Joubaud, and A. Petrosyan, Entropy Production and Time Asymmetry in Nonequilibrium Fluctuations, Phys. Rev. Lett. 98 (2007) 150601. • D. Andrieux, P. Gaspard, S. Ciliberto, N. Garnier, S. Joubaud, and A. Petrosyan, Thermodynamic time asymmetry in non-equilibrium fluctuations, J. Stat. Mech.: Th. & Exp. (2008) P01002. • D. Andrieux and P. Gaspard, Fluctuation theorem and Onsager reciprocity relations, J. Chem. Phys. 121 (2004) 6167. • D. Andrieux and P. Gaspard, Fluctuation theorem for transport in mesoscopic systems, J. Stat. Mech. (2006) P01011. • D. Andrieux and P. Gaspard, Fluctuation theorem for currents and Schnakenberg Network Theory, J. Stat. Phys. 127 (2007) 107. • D. Andrieux and P. Gaspard, A fluctuation theorem for currents and non-linear response coefficients, J. Stat. Mech. (2007) P02006. • D. Andrieux, P. Gaspard, T. Monnai, and S. Tasaki, The fluctuation theorem for currents in open quantum systems, New J. Phys. 11 (2009) 043014.

Speaker: Prof. Pierre Gaspard (Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles)

14:00 → 14:45 Out of equilibrium fluctuation induced forces

Speaker: Prof. David Dean (Laboratoire de Physique Théorique, Université Paul Sabatier, Toulouse)

14:45 → 15:00 Coffee

15:00 → 15:45 Momentum transfer in non-equilibrium steady states

We introduce a new approach to investigate the steady state velocity of Brownian objects in dissipative setups. We extract the momentum transfer that is directly associated to the steady state velocity of the Brownian object. This approach provides simple physical explanation why, for example, the adiabatic piston moves toward hot side. Similarly it explains the direction of steady state velocity of certain Brownian motors. This work has been submitted (Antoine Fruleux, Ryoichi Kawai and KS, 10 Aug. 2011).

Speaker: Prof. Ken Sekimoto (Lab. Matières et Systèmes Complexes, Université Paris Diderot)

18:00 → 20:00 Conference dinner

Thursday, 29 September

09:30 → 10:00 Coffee

10:00 → 10:45 Lagrangian phase transitions in nonequilibrium thermodynamic systems

Speaker: Prof. Giovanni Jona-Lasinio (Physics Department, Sapienza University of Rome)

10:45 → 11:30 Additivity Principle in High-dimensional Deterministic Systems

The additivity principle (AP), conjectured by Bodineau and Derrida is discussed for the case of heat conduction in three-dimensional disordered harmonic lattices to consider the effects of deterministic dynamics, higher dimensionality, and different transport regimes, i.e., ballistic, diffusive, and anomalous transport. The cumulant generating function (CGF) for heat transfer is accurately calculated using the formal expression derived recently. We compare the CGF for harmonic crystals with the one given by the AP. In the diffusive regime, we find a clear agreement with the conjecture even if the system is high-dimensional. Surprisingly even in the anomalous regime the CGF is also well fitted by the AP. Lower dimensional systems are also studied and the importance of three-dimensionality for the validity is stressed.

Speaker: Prof. Keiji Saito (Department of Physics, University of Tokyo)

14:00 → 14:45 Large deviation functions and fluctuation theorems in heat transport

The large deviation function contains information on the probability of rare fluctuations of a stochastic variable. In this talk the large deviation function for heat transport in harmonic systems will be discussed. Results on the analytic and numerical computation of the large deviation function will be described.

Speaker: Prof. Abhishek Dhar (Raman Research Institute, Bangalore)

15:00 → 16:00 Coffee

Friday, 30 September

09:30 → 10:00 Coffee

10:00 → 10:45 A stochastic model of anomalous heat conduction

We review the problem of anomalous conductivity in one-dimensional system and discuss a simple stochastic model where those properties can be studied exactly.

Speaker: Prof. Stefano Lepri (Istituto dei Sistemi Complessi, Unita Operativa di Firenze)

10:45 → 11:30 Nonequilibrium fluctuations and thermodynamics for electron transport through small devices

Fluctuations in electronic currents crossing small devices can be nowadays resolved at the single electron level. I will present exact relations, called fluctuation theorems, which impose universal constraints on these current fluctuations and which can be seen as a far-from-equilibrium generalizations of fluctuation-dissipation relations. I will also show that these relations can help us establish a thermodynamic description of transport which can be used for example to study the efficiency of thermoelectric energy conversion far-from-equilibrium.

Speaker: Dr Massimiliano Esposito (Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles)

15:00 → 18:00 Reception

Monday, 3 October

09:00 → 10:00 Welcome breakfast & Registration

10:00 → 10:45 First-passage times for single-file diffusion and fractional Langevin dynamics

There is an increasing amount of interest in the problem of INTERACTING random walkers (due to the strong connection of this problem to the fields of, for instance, biophysics, nanofluidics, and cell biology). We have focused on the non-equilibrium problem of interacting walkers in (quasi)one dimensional systems, so called single-file diffusion (SFD), where we recently showed that the tracer paricle motion in an SFD system belong to the same universality class as that of fractional Langevin dynamics [1]. An interesting, not yet fully understood, problem in this field is that of first-passage times for this type of non-Markovian dynamics. We have investigated the first passage time densities (FPTD) of a tracer particle in a SFD system whose population is: (i) homogeneous i.e. all particles having the same dffusion constant and (ii) heterogeneous with diffusion constants drawn from a heavy-tailed power-law distribution. Extensive stochastic SFD simulations are performed and compared to two analytical estimates: the Method of Images approximation (MIA) and the Willemski-Fixman approximation (WFA). We find that the MIA cannot approximate well any temporal scale of the FPTD. Our exact inversion of the Willemski-Fixman integral equation captures the long-term power-law exponent predicted by Molchan [1999] for fractional Brownian motion for certain Hurst exponents. A simple new functional form is proposed to describe the FPTD for all times, and to guide further research into this phenomenon. [1] T. Ambjornsson, L. Lizana, A. Taloni, E. Barkai and M.A. Lomholt, Foundation of fractional Langevin equations: Harmonization of a many-body problem, Phys. Rev. E 81, 051118 (2010). [2]. L. P. Sanders and T. Ambjornsson, in preparation.

Speaker: Tobias Ambjörnsson (Computational Biology and Biological Physics, Lund University)

10:45 → 11:30 Anomalous diffusion for a class of Hamiltonian systems with two conserved quantities

We introduce a class of one dimensional Hamiltonian systems with two conservation laws. Numerical simulations show that these dynamics are genuinely super-diffusive. We then modify the dynamics by adding a conservative stochastic noise so that it becomes ergodic. System of conservation laws are derived as hydrodynamic limits of the modified dynamics. Numerical evidence shows these models are still super-diffusive. This is proven rigorously for harmonic potentials and exponential interactions.

Speaker: Cedric Bernardin (École Normale Supérieure de Lyon)

15:00 → 16:00 Coffee

Tuesday, 4 October

09:30 → 10:00 Coffee

10:00 → 10:45 Mechanisms of Formation of Signaling Molecules Concentration Profiles

Concentration profiles of signaling molecules, also known as morphogen gradients, play a critical role in the development of multicellular organisms by determining polarity and spatial patterning that leads to further tissue differentiation. Large advances in studying morphogen gradients have been achieved recently when the formation of signaling molecules profiles has been visualized with high temporal and spatial resolution. A widely used approach to explain the establishment of concentration gradients assumes that signaling molecules are produced locally, then spread via a free diffusion and degraded uniformly. However, recent experiments have produced controversial observations concerning the feasibility of this theoretical description. In addition, latest theoretical analysis of times to establish the morphogen gradient yield surprising linear scaling as a function of length, not expected for the systems with unbiased diffusion process. We propose here a theoretical approach that provides a possible microscopic explanation of these observations. It is argued that relaxation times are mostly determined by first-passage times and the degradation effectively accelerates diffusion of signaling particles by removing slow moving molecules. Our theoretical analysis indicates that spatial and temporal features of degradation mechanisms mostly control the establishment of signaling molecules profiles.

Speaker: Prof. Anatoly Kolomeisky (Department of Chemistry, Rice University)

10:45 → 11:30 Record statistics in time series with drift: Theory and applications

Record-breaking events of all kinds generate considerable attention in the public domain, but the mathematical theory of records appears to be known only to specialists. In its classic form, the theory is concerned with records in time series of independent, identically distributed random variables, for which the sequence of record-breaking events displays a number of non-obvious, universal properties. In recent work we have modified the basic record model by taking into account a systematic, linear time dependence of the mean of the underlying random variables. Somewhat counterintuitively, the drift induces correlations between record events which may lead to a bunching of records when the underlying probability distribution has heavy tails. Applications of the theory to global warming and stock market fluctuations will also be described. The talk is based on joint work with Gregor Wergen and Jasper Franke.

Speaker: Prof. Joachim Krug (University of Cologne)

15:00 → 16:00 Coffee

Wednesday, 5 October

09:30 → 10:00 Coffee

10:00 → 10:45 Current fluctuations: mapping non-equilibrium to equilibrium

Interacting classical particles diffusing in 1d have provided in recent years an interesting playground to study non-equilibrium. The dynamics of these models is described by an evolution operator, which can be written as a spin chain Hamiltonian H. One is interested in the steady state properties and in the probability that the system presents an atypical current flow. These are described by large deviation functions (ldf). Finding the ldf amounts to determining the ground state of H -- a correspondence which provides an interesting bridge between classical and quantum problems. I will present different methods (Bethe Ansatz, fluctuating hydrodynamics) used to compute the ldf and to characterize its singularities -- which correspond to dynamical phase transitions. Some class of systems also present an intriguing duality between non-equilibrium and equilibrium, that enlight for instance the existence of long-range correlations induced by e.g. contact with reservoirs of different chemical potential.

Speaker: Vivien Lecomte (Université Paris Diderot)

10:45 → 11:30 Nonequilibrium Stationary States of Harmonic Chains with Bulk Noises

In a joint work with C.Bernardin, J.L.Lebowitz, and V.Kannan, we consider a chain composed of N coupled harmonic oscillators in contact with heat baths at its end points. The oscillators are also subjected to non-momentum conserving bulk stochastic noises. These make the heat conductivity satisfy Fourier's law. We describe some new results about the hydrodynamical equations for typical macroscopic energy and displacement profiles, as well as their fluctuations and large deviations, in two simple models of this type.

Speaker: Prof. Jani Lukkarinen (University of Helsinki)

15:00 → 16:00 Coffee

18:00 → 20:00 Conference dinner

Thursday, 6 October

09:30 → 10:00 Coffee

10:00 → 10:45 Asymmetric granular motors: Does the ratchet effect persist in the presence of friction?

Several recent theoretical studies of idealized models of granular motors, which use a Boltzmann-Lorentz description [1, 2, 3, 4, 5, 6], show that the motor effect is particularly pronounced when the device is constructed from two different materials, as was the case in a recent experiment [7]. The existing theories, however, predict a motor effect for any temperature of the granular gas while in the experiment the phenomenon is only observed if the bath temperature is sufficiently large. The presence of friction is at the origin of this difference and it is therefore highly desirable to incorporate it in the theoretical schemes. Within the framework of a Boltzmann-Lorentz equation, we analyze the dynamics of a granular rotor immersed in a bath of thermalized particles in the presence of a dynamic frictional torque on the axis [8]. In numerical simulations of the equation, we observe two scaling regimes at low and high bath temperatures. In the large friction limit, we obtain the exact solution of a model corresponding to asymptotic behavior of the Boltzmann-Lorentz equation. In the limit of large rotor mass and small friction, we derive a Fokker-Planck equation for which the exact solution is also obtained. Finally, we consider the influence of a static dry friction. [1] B. Cleuren and C. V. den Broeck, Europhys. Lett. 77, 50003 (2007) [2] G. Costantini, U. M. B. Marconi, and A. Puglisi, Phys. Rev. E 75, 061124 (2007) [3] B. Cleuren and R. Eichhorn, J. Stat. Mech. 2008, P10011 (2008) [4] G. Costantini, U. Marini Bettolo Marconi, and A. Puglisi, Europhys. Lett. 82, 50008 (2008) [5] J. Talbot, A. Burdeau, and P. Viot, Phys. Rev. E 82, 011135 (2010) [6] J. Piasecki, J. Talbot, and P. Viot, J. Stat. Mech. 2010, P05004 (2010) [7] P. Eshuis, K. van der Weele, D. Lohse, and D. van der Meer, Phys. Rev. Lett. 104, 248001 (2010) [8] J. Talbot, R. D. Wildman, and P. Viot, “Kinetics of a frictional granular motor,” To appear in Phys. Rev. Lett.

Speaker: Pascal Viot (Paris)

10:45 → 11:30 Exact nonequilibrium steady state of a strongly driven open XXZ chain

An exact and explicit ladder-tensor-network ansatz is presented for nonequilibrium steady state of an anisotropic Heisenberg XXZ spin-1/2 chain which is driven far from equilibrium with a pair of Lindblad operators acting on the edges of the chain only. We show that the steady-state density operator of a finite system of size $n$ is -- apart from a normalization constant -- a polynomial of degree 2n-2 in the coupling constant. Efficient computation of physical observables is facilitated in terms of a transfer-operator reminiscent of a classical Markov process. In the isotropic case we find cosine spin profiles, 1/n^2 scaling of the spin current, and long-range correlations in the steady state.

Speaker: Prof. Tomaz Prosen (Department of Physics, University of Ljubljana)

15:00 → 16:00 Coffee

Friday, 7 October

09:30 → 10:00 Coffee

10:00 → 10:45 Diffusion with stochastic resetting

"Stochastic resetting" is a rather common process in everyday life. Consider searching for some target such as, for example, a face in a crowd or one?s misplaced keys at home. A natural tendency is, on having searched unsuccessfully for a while, to return to the starting point and recommence the search. In this talk I explore the consequences of such resetting on perhaps the most simple and common process in nature, namely, the diffusion of a single or a multiparticle system. It turns out that a nonzero rate of resetting has a rather rich and dramatic effect on the diffusion process, strongly affecting the behaviour of mean first passage times and survival probabilities.

Speaker: Prof. Martin Evans (Edinburgh)

10:45 → 11:30 Large deviations of the current in collisional dynamics

We argue that the large deviations of the current in a class of deterministic collisional dynamics display an usual behavior.

Speaker: Prof. Raphael Lefevere (Université Paris Diderot)

15:00 → 18:00 Reception

Monday, 10 October

09:00 → 10:00 Welcome breakfast & Registration

10:00 → 10:45 Motion in an aging environment

n the talk I will discuss motion in an environment, where each location only allows motion at random discrete time points separated by power law distributed random time intervals. As an example one can think of a network of bus or train routes with erratic arrival times. We find that for heavy-tailed power laws the motion through the environment becomes logarithmicly slow. Surprisingly the uncertainty in the location grows slower than the relative position. The original motivation of the work was the study of single files of subdiffusive continuous time random walkers. In the talk I will present scaling arguments for the mean square displacement of a tagged particle in such a file.

Speaker: Prof. Michael A. Lomholt (MEMPHYS - Center for Biomembrane Physics, University of Southern Denmark)

10:45 → 11:30 Ecosystems with mutually exclusive interactions

Ecological systems comprise an astonishing diversity of species that cooperate or compete with each other forming complex mutual dependencies. The minimum requirements to maintain a large species diversity on long time scales are in general unknown. Using lichen communities as an example, we propose a model for the evolution of mutually excluding organisms that compete for space. We suggest that chain-like or cyclic invasions involving three or more species open for creation of spatially separated sub-populations that subsequently can lead to increased diversity. In contrast to its non-spatial counterpart, our model predicts robust co-existence of a large number of species, in accordance with observations on lichen growth. It is demonstrated that large species diversity can be obtained on evolutionary timescales, provided that interactions between species have spatial constraints. In particular, a phase transition to a sustainable state of high diversity is identified. Reference: J. Mathiesen, N. Mitarai, K. Sneppen and A. Trusina arXiv:1108.2011 , accepted for publication in Phys. Rev. Lett.

Speaker: Prof. Namiko Mitarai (Niels Bohr Institute, Copenhagen)

15:00 → 16:00 Coffee

Tuesday, 11 October

09:30 → 10:00 Coffee

10:00 → 10:45 Modified fluctuation-dissipation theorem near non- equilibrium states and applications

In small systems, like molecular motors, thermodynamic quantities like work or heat are only defined in a statistical sense. Exact relations between the statistical distributions of these quantities, known as fluctuations relations, have been obtained about a decade ago. Within the linear regime, these fluctuations relations lead to interesting modified fluctuation dissipation theorems valid for systems close to non-equilibrium states and obeying markovian dynamics. We will discuss two different generalizations: in the first one, the unperturbed system is in a non-equilibrium steady state [1], whereas in the second one, it is in a non-equilibrium non-steady state [2]. For these two situations, we will illustrate our framework with examples based on solvable models. We will use a simple model of molecular motors for the first case [1], and two examples for the second case : a system obeying linear Langevin dynamics and the 1D Ising model with Glauber dynamics submitted to a quentch of temperature [2]. [1] Modified fluctuation-dissipation theorem for non-equilibrium steady states and applications to molecular motors, G. Verley, K. Mallick and D. Lacoste, Europhys. Lett., 93, 10002 (2011). [2] Modified fluctuation-dissipation theorem near non-equilibrium states and applications to the Glauber-Ising chain, G. Verley, R. Chétrite, D. Lacoste, http://fr.arxiv.org/abs/1108.1135

Speaker: Prof. David Lacoste (Laboratoire de Physico-Chimie Théorique, ESPCI)

10:45 → 11:30 Conductance of quasi one-dimensional periodic systems and current in a one-dimensional non equilibrium quantum system

Speaker: Prof. Felipe Barra (Departamento de Fisica, Universidad de Chile)

15:00 → 16:00 Coffee

Wednesday, 12 October

09:30 → 10:00 Coffee

10:00 → 10:45 Single particle trajectories and time averages in ageing systems with weak ergodicity breaking

Speaker: Prof. Ralf Metzler (Physik Department, Technical University of Munich)

10:45 → 11:30 Metapopulation dynamics

discuss the population dynamics of metapopulations consisting of many small local populations coupled by migration. By means of analytical calculations and direct numerical simulations of the stochastic population dynamics I address the question: what is the most likely path to extinction? With A. Eriksson (Cambridge University) and F. Elias Wolff (University of Gothenburg). An overview of metapopulation dynamics is given in the review article by Hanski [1]. [1] Ilkka Hanski, Nature 396, 41 (1998)

Speaker: Prof. Bernhard Mehlig (University of Gothenburg)

15:00 → 16:00 Coffee

18:00 → 20:00 Conference dinner

Thursday, 13 October

09:30 → 10:00 Coffee

10:00 → 10:45 Sinai diffusion with weakly concentrated absorbers

Speaker: Prof. Christophe Texier (Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud)

10:45 → 11:30 Fluctuating hydrodynamics for a driven granular fluid: out of equilibrium correlations

Speaker: Giacomo Gradenigo (Physics Department, Sapienza University of Rome)

15:00 → 16:00 Coffee

Friday, 14 October

09:30 → 10:00 Coffee

10:00 → 10:45 Long-range correlations in driven, nonequilibrium systems

The interplay between the statistical properties of non-equilibrium systems systems with long-range interactions in equilibrium will be discussed. Driven systems tend to exhibit long-range correlations, resulting from the non detailed balance nature of their dynamics. Such correlations can sometimes be expressed by effective long-range interactions, even in cases where the dynamics is local. On the other hand studies of equilibrium systems with long-range interactions have demonstrated that they exhibit some unusual properties, such as inequivalence of statistical ensembles, negative specific heat and slow relaxation processes, with diverging characteristic time with the system size. Such features in driven systems with local dynamics will be demonstrated and some similarities between these two classes of systems will be discussed.

Speaker: Prof. David Mukamel (Department of Physics of Complex Systems, The Weizmann Institute of Science)

15:00 → 18:00 Reception