Stochastic Thermodynamics



Erik Aurell (KTH), Ralf Eichhorn (Nordita)


Nordita, Stockholm, Sweden


Stochastic Thermodynamics represents an exciting new research direction in statistical physics, which explores fundamental aspects of non-equilibrium processes. The developments summarized under this term may be characterized by the common idea to adapt and generalize concepts from equilibrium thermodynamics to the non-equilibrium realm, typically on the level of single particle trajectories monitored over the entire system evolution. This approach has proven to be quite powerful and produced results of remarkable generality —e.g. so-called fluctuation theorems— connecting the system behavior when driven out of equilibrium with its equilibrium properties. This program intends to bring together the experts in the field in order to discuss open questions and new ideas in a lively and intensive atmosphere provided at Nordita.


We aim at having two presentations per day with plenty of time for discussions and project work in a relaxed atmosphere.

Confirmed Participants

  • Antonio Celani, Institut Pasteur, Paris
  • Sergio Ciliberto, University of Lyon
  • Bart Cleuren, Hasselt University
  • Eddy Cohen, Rockefeller University
  • Massimiliano Esposito, Luxembourg University
  • Krzysztof Gawedzki, ENS Lyon
  • Ryoichi Kawai, University of Alabama at Birmingham
  • Jorge Kurchan, University of Paris
  • David Lacoste, ESPCI, Paris
  • Katja Lindenberg, University of California, San Diego
  • Juan Parrondo, Madrid University
  • Jukka Pekola, Aalto University School of Science
  • Felix Ritort, University of Barcelona
  • Lamberto Rondoni, Politecnico di Torino
  • Shin-ichi Sasa, Unversity of Tokio
  • Udo Seifert, Stuttgart University
  • Angelo Vulpiani, Universita di Roma "La Sapienza", Rome


Application for participation in the program is closed.

A minimum stay of one working week is required and we encourage participants to stay for the whole two-weeks period of the program.

There is no conference fee.

Travel Reimbursement

PhD students and young Postdoc fellows are eligible for travel grants to participate in the program. If you are interested in such a grant, please mark the corresponding field in the application form, briefly summarize your interest in the program in the comments field, and indicate an estimation of your expected travel expenses. Since only a limited number of grants is available, decision concerning the grants will be made on a case-by-case basis and you will be notified shortly after the application deadline.


Nordita provides a limited number of rooms in the Stockholm apartment hotel BizApartments free of charge for accepted program participants, who stay at least one week.

Sponsored by:


  • Aki Kutvonen
  • Alberto Imparato
  • Alexander Balatsky
  • Alexander Mozeika
  • Angelo Vulpiani
  • Antonio Celani
  • Arnab Pal
  • Astrid S. de Wijn
  • Bart Cleuren
  • Carlos Mejia-Monasterio
  • Claudia Battistin
  • Daniel Rings
  • Dario Villamaina
  • David LACOSTE
  • E.G.D. Cohen
  • Edwin Langmann
  • Erik Aurell
  • Felix Ritort
  • Gatien Verley
  • Gino Del Ferraro
  • Göran Lindblad
  • Ingemar Bengtsson
  • Irene Donato
  • Jorge Kurchan
  • Juan MR Parrondo
  • Jukka Pekola
  • Katja Lindenberg
  • Kiyoshi Kanazawa
  • Krzysztof Gawedzki
  • Kyogo Kawaguchi
  • Lamberto Rondoni
  • Léo Granger
  • Marcus-Alexander Assmann
  • Martin Rosinberg
  • Massimiliano Esposito
  • Matteo Polettini
  • Mikko Vehkaperä
  • Mélanie ROLLES
  • Natalia Golubeva
  • Nicolas Innocenti
  • Paolo De Gregorio
  • Ralf Eichhorn
  • Roman Belousov
  • Ryoichi Kawai
  • Rémi Lemoy
  • Samu Suomela
  • Sergio Ciliberto
  • Shin-ichi Sasa
  • Sorin Tanase Nicola
  • Stefano Bo
  • Takahiro Nemoto
  • Timo Koski
  • Tobias Brett
  • Udo Seifert
  • Yohei Nakayama
    • 10:00 AM 11:00 AM
      Small Systems: a challenge for the Statistical Mechanics 1h
      The energy of a finite system thermally connected to a thermal reservoir may fluctuate, while the temperature is a constant representing a thermodynamic property of the reservoir. The finite system can also be used as a thermometer for the reservoir. From such a perspective the temperature has an uncertainty, which can be treated within the framework of estimation theory. We review the main results of this theory, and clarify some controversial issues regarding temperature fluctuations. We also offer a simple example of a thermometer with a small number of particles. We discuss the relevance of the total observation time, which must be much longer than the decorrelation time. In addition some preliminar results on partitioning systems will be discussed. Ref.s: M. Falcioni, D. Villamaina, A. Vulpiani, A. Puglisi and A. Sarracino "Estimate of temperature and its uncertainty in small systems" Am. J. Phys. 79, 777 (2011) E. DelRe, B. Crosignani, P. Di Porto and S. Di Sabatino "Built-in reduction of statistical fluctuations of partitioning objects" Phys. Rev. E 84, 021112 (2011)
      Speaker: Prof. Angelo Vulpiani (Dep. of Physics, Universita Sapienza di Roma)
    • 3:00 PM 4:00 PM
      Stochastic thermodynamics of autonomous information machines: From Maxwell's demons to cellular sensing 1h
      The framework of stochastic thermodynamics can be applied to Brownian information machines for which information about the system acquired in a measurement is used to extract work from a single heat bath. Fluctuation theorems have been generalized to such feedback-driven non-autonomous machines following an almost standard recipe also allowing to discuss their efficiency and efficiency at maximum power. After briefly recalling this (reasonably well-understood) class, I will describe our recent work dealing with autonomous machines. First, I will discuss a fully stochastic, reversible variant of the demon recently introduced by Mandal and Jarzynski [PNAS 109, 11641, 2012]. Our generalization which includes genuine equilibrium allows to identify Onsager coefficients and the linear response theory of such a demon [1]. Second, within a minimal model for cellular sensing, I will discuss the relation between information-theoretic and thermodynamic entropy production. While one could naively expect the rate of information to be bounded by the thermodynamic cost of acquiring it, based on our new bound on the rate of mutual information for time-continuous processes, I will show that there is no such inequality [2]. [1] AC Barato and US, arXiv:1302.3089 [2] AC Barato, D. Hartich and US, arXiv:1212.3186
      Speaker: Prof. Udo Seifert (Univ. Stuttgart)
    • 10:00 AM 11:00 AM
      Remarks on the Jarzynski and Crooks Theorems 1h
      A discussion will be presented of the Jarzynski and Crooks Theorems and their relation to the stretching experiments of RNA in water.
      Speaker: Prof. E.G.D. Cohen (Rockefeller University)
    • 3:00 PM 4:00 PM
      Fluctuation relation for weakly ergodic aging systems 1h
      A fluctuation relation for aging systems is introduced and verified by extensive numerical simulations. It is based on the hypothesis of partial equilibration over phase-space regions in a scenario of entropy-driven relaxation. The relation provides a simple alternative method, amenable of experimental implementation, to measure replica symmetry breaking parameters in aging systems. The connection with the effective temperatures obtained from the fluctuation-dissipation theorem is discussed.
      Speaker: Prof. Felix Ritort (Universitat de Barcelona)
    • 10:00 AM 11:00 AM
      Stochastic thermodynamics for adiabatic pistons 1h
      Suppose that a box is divided into two regions by an adiabatic and movable wall, gases are confined in the two regions, and that the whole system is isolated. In this special setting, the equilibrium state is not determined from the variational principle of thermodynamics. To discuss phenomena in related settings is known as the adiabatic piston problem. In particular, various arguments in kinetic theory, mathematical physics, and non-equilibrium physics have been proposed since 1999 when Lieb presented the importance of the problem. Here, the understanding of fluctuation of the wall position plays an important role in the problem, and hence the thermodynamic argument should be developed on the basis of ``stochastic thermodynamics''. In my presentation, I carefully describe the heart of the problem. I then analyze a system under the condition that pressures and temperatures at the both ends are kept constant. I also address open questions, some of which might be expected to be solved in the workshop. (This work is done in collaboration with M. Itami.)
      Speaker: Prof. Shin-ichi Sasa (Kyoto University)
    • 3:00 PM 4:00 PM
      On the heat flux and entropy produced by thermal fluctuations 1h
      We report an experimental and theoretical analysis of the energy exchanged between two conductors kept at different temperature and coupled by the electric thermal noise. This system is probably the simplest example to test recent ideas of stochastic thermodynamics, but in spite of its simplicity the explanation of the observations is far from trivial. Experimentally we determine, as functions of the temperature difference, the heat flux, the out-of-equilibrium variance and a conservation law for the fluctuating entropy, which we justify theoretically. The system is ruled by the same equations of two Brownian particles kept at different temperatures and coupled by an elastic force. Our results set strong constrains on the energy exchanged between coupled nano-systems kept at different temperature
      Speaker: Prof. Sergio Ciliberto (CNRS Ecole Normale Supérieure de Lyon)
    • 10:00 AM 11:00 AM
      Macroscopic fluctuations in out of equilibrium systems with mean field interactions 1h
      I shall discuss the non-equilibrium Langevin dynamics of N identical systems with a mean field coupling, governed for N infinite by the non-linear Fokker-Planck equation. For large but finite N, the fluctuations around the solutions of that equation are described by the large deviation theory of the Rome school and may be controled analytically in perturbation theory.
      Speaker: Dr Krzysztof Gawedzki (Ecole Normale de Lyon)
    • 3:00 PM 4:00 PM
      Stochastic Energetics with electrons in a circuit 1h
      I discuss distribution of dissipation, fluctuation theorems and Maxwell's demon in single-electron transport and in superconducting quantum circuits. Special emphasis is on experiments in nanocircuits and on experimentally feasible scenarios of testing quantum fluctuation relations.
      Speaker: Prof. Jukka Pekola (Aalto University School of Science)
    • 10:00 AM 11:00 AM
      Finite Time Thermodynamics of Simple Model Systems 1h
      A variety of simple model systems provide a theoretical testbed for a thorough characterization of the efficiency of operation of thermodynamic systems at maximum power (i.e., away from equilibrium) and also for the characterization of fluctuations in small thermodynamics systems in a non-equilibrium steady states. These models are particularly attractive because they can be explored analytically. Starting with idealized single quantum dot devices we will present a variety of such systems in a variety of operational modes. Our goal is to understand universal properties beyond the linear response regime.
      Speaker: Prof. Katja Lindenberg (University of California)
    • 2:00 PM 4:00 PM
      Jam Session 2h
      Speakers: Mr Aki Kutvonen (Aalto University), Mr Arnab Pal (Raman Research Institute), Dr Daniel Rings (University Leipzig), Mr Kyogo Kawaguchi (University of Tokyo), Ms Natalia Golubeva (Aarhus University), Mr Takahiro Nemoto (Kyoto University), Mr Yohei Nakayama (University of Tokyo)
    • 10:00 AM 11:00 AM
      Stochastic Thermodynamics and Information Processing 1h
      I will start by presenting different ways in which one can use stochastic thermodynamics to characterize the cost of operations manipulating information. The main focus of my talk will be dedicated to explicitly show, using stochastic thermodynamics, in what sense a Maxwell demon effectively modifies the second law of thermodynamics and in what sense it satisfies the second law when the cost for operating the demon is taken into account. A model of coupled quantum dots will be used to illustrate my point.
      Speaker: Dr Massimiliano Esposito (University of Luxembourg)
    • 3:00 PM 4:00 PM
      Carnot cycle for isothermal energy conversion 1h
      Transforming one form of work into a different form can be done with 100% efficiency. This upper limit has no practical relevance since it requires a reversible operation and hence leads to a zero power output. In this talk I will consider a number of transformation processes and discuss the features of efficiency at maximum power output.
      Speaker: Prof. Bart Cleuren (Hasselt University)
    • 10:00 AM 11:00 AM
      Deterministic Approach to Nonequilibrium Physics: news from RareNoise 1h
      Twenty years ago, the molecular dynamics approach to nonequilibrium phenomena gave birth to a vast still growing wave of investigations, which has resulted in a number of works conceptually important in general, and of practical relevance especially in the mesoscopic realm. That wave has largely turned towards stochastic systems, considered easier to handle. We will outline recent results on non-equilibrium response, obtained from the deterministic (molecular dynamics/dynamical systems) perspective, which complements the stochastic perspective. Relaxation, response relations and optimal controlwill be considered, together with a new interpretation of nonquilibrium effective temperatures. These results raise some new questions on the use of ergodic theory in statistical mechanics.
      Speakers: Prof. Lamberto Rondoni (Politecnico di Torino), Dr Paolo De Gregorio (INFN Padova)
    • 3:00 PM 4:00 PM
      The entropic anomaly 1h
      Particle motion at the micro-scale is an incessant tug-of-war between thermal fluctuations and applied forces on one side, and the strong resistance exerted by fluid viscosity on the other. Friction is so strong that completely neglecting inertia – the overdamped approximation – gives an excellent effective description of the actual particle mechanics. In sharp contrast with this result, here we show that the overdamped approximation dramatically fails when thermodynamic quantities such as the entropy production in the environment is considered, in presence of temperature gradients. In the limit of vanishingly small, yet finite inertia, we find that the entropy production features a contribution that is anomalous, i.e. has no counterpart in the overdamped approximation. This phenomenon, that we call entropic anomaly, is due to a symmetry-breaking that occurs when moving to the small, finite inertia limit. As a consequence of this phenomenon, quasi-static engines, whose efficiency is maximal in a fluid at uniform temperature, have in fact vanishing efficiency in presence of temperature gradients. For slow cycles the efficiency falls off as the inverse of the period. The maximum efficiency is reached at a finite value of the cycle period that is inversely proportional to the square root of the gradient intensity. The relative loss in maximal efficiency with respect to the thermally homogeneous case grows as the square root of the gradient. As an illustration of these general results, we construct an explicit, analytically solvable example of a Carnot stochastic engine. In this thought experiment, a Brownian particle is confined by a harmonic trap and immersed in a fluid with a linear temperature profile. This example may serve as a template for the design of real experiments in which the effect of the entropic anomaly can be measured. Antonio Celani, Stefano Bo, Ralf Eichhorn, and Erik Aurell, Phys. Rev. Lett. 109, 260603 (2012) Stefano Bo and Antonio Celani, arXiv:1212.1608
      Speaker: Prof. Antonio Celani (CNRS - Institut Pasteur)
    • 10:00 AM 11:00 AM
      Adiabatic Piston and Momentum Deficit due to Dissipation: From Hydrodynamics Perspective 1h
      A Brownian piston separating two gases of different temperature mediates heat transfer from one gas to the other via its velocity fluctuations. Such heat transfer is well understood at the Langevin theory. However, the gases in turn exert non-equilibrium force on the piston. Such a force is responsible for various intriguing non-equilibrium processes such as adiabatic piston and a certain types of Brownian motors. It has been shown that the standard linear Langevin theory fails to explain the force. The Master-Boltzmann approach beyond the Langevin description successfully predicted the force but it did not reveal the physical origin of the force. Recently, Freleux et al [PRL 108, 160601 (2012)] introduced the new concept of momentum deficit due to dissipation (MDD) and showed that it can explain the origin of the force with a few lines of calculation only based on the energy and momentum conservation laws. However, all previous theories including the MDD assume that the gas particles hitting the piston are taken from an equilibrium velocity distribution and outgoing particles disappears without colliding with the incoming particles. Since the outgoing particles are not in a thermal equilibrium due to dissipation, their collision with the incoming particles disturbs the velocity distribution of the incoming particles, invalidating the assumption used in the previous theories. Therefore, I would like to discuss the MDD from the hydrodynamics point of view. When a nonequilibrium steady state is established, we can show that the heat and momentum fluxes in the gases satisfy the MDD condition such that energy and momentum transport in hydrodynamics is consistent with the MDD theory of adiabatic piston.
      Speaker: Prof. Ryoichi Kawai (University of Alabama at Birmingham)
    • 3:00 PM 4:00 PM
      Stochastic modeling of weakly chaotic systems 1h
      Integrable systems become chaotic as soon as one perturbs them with an external, additive random noise. The Lyapunov exponents are a power law of the noise intensity. The regime being by nature beyond the Kolmogorov Arnold Moser (and also the Nekhoroshev) regimes, it offers us a glimpse of the behavior of weakly chaotic deterministic systems, in an multi-resonance situation.
      Speaker: Prof. Jorge Kurchan (LPS-Ecole Normale superieure)
    • 10:00 AM 11:00 AM
      Information motors vs chemical motors 1h
      To induce transport, detailed balance must be broken. A common mechanism is to bias the dynamics with a thermodynamic fuel, such as chemical energy. An intriguing, alternative strategy is for a Maxwell demon to effect the bias using information and feedback. In this seminar I will review the thermodynamics of information and present two systems, a chemical motor and an information motor, exhibiting the same dynamical behavior but with very different thermodynamical properties. The analysis of these motors elucidates the manner in which information is incorporated into a physical system.
      Speaker: Prof. Juan Parrondo (Universidad Complutense de Madrid)
    • 3:00 PM 4:00 PM
      Dissipation in simple non-equilibrium model systems 1h
      Stochastic thermodynamics is a framework for extending notions of classical thermodynamics to the level of individual trajectories which can be recorded in non-equilibrium conditions. While this framework is well established for stochastic systems described by markovian processes, the situation is less well understood when the strength of the noise depends on the driving or when non-markovian dynamics is involved. Such situations are not purely academic but arise in soft matter or biological systems. In the first part of the talk, I will present an experimental study of a model system made of magnetic colloidal particles which are manipulated using a time-dependent magnetic field. By recording the trajectories of the colloidal particles, the distributions of thermodynamic quantities such as work or heat can be obtained. This experiment is interesting because (i) it involves state dependent hydrodynamic friction and (ii) it can be carried out with more than one degree of freedom. In the second part of this talk, I will review a set of formal results which we obtained recently by generalizing the Hatano-Sasa relation to systems which have been prepared initially in a non-stationary non-equilibrium state. Such results include a generalized fluctuation-dissipation theorem and second-law like inequalities for non-equilibrium systems.
      Speaker: Dr David Lacoste (ESPCI)
    • 10:00 AM 12:30 PM
      Jam Session 2h 30m