Current and Future Trends in Stochastic Thermodynamics

4 Sept 2017, 09:00 → 29 Sept 2017, 18:00 Europe/Stockholm

122:026 (Nordita, Stockholm)

Astrid de Wijn (Stockholm University), Bart Cleuren (Hasselt University), Erik Aurell (KTH), Ralf Eichhorn (Nordita)

Venue

Nordita, Stockholm, Sweden

Scope

Stochastic thermodynamics is a recently established discipline of statistical physics. It aims to apply and extend thermodynamic principles to the non equilibrium regime. In particular, it provides an adequate framework to investigate the behaviour of small systems. The salient property of stochastic thermodynamics is the incorporation of fluctuations, which are prominent on that scale. In combination with the constraints put forth by macroscopic thermodynamics, a number of important fundamental results were established, e.g. the fluctuation theorems. Stochastic thermodynamics is by now a rapidly evolving field, with an increasing range of applications. The aim of this program to discuss the latest developments and open problems in Stochastic Thermodynamics.

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[Timetable - available from start of the program]

Format

The main objective is to create a lively and fruitful atmosphere of research and mutual interactions, and to initiate new collaborations. We have in mind an informal and inspiring program with two presentations per day, one in the mornings and one in the (early) afternoon, highlighting recent exciting results, open problems or unsolved puzzles, that may serve as "condensation nuclei" for subsequent discussion session and project work in the periods in between and after the talks.

Application

If you want to apply for attending the program, please fill in the application form. You will be informed by the organizers shortly after the application deadline whether your application has been approved. Due to space restrictions, the total number of participants is strictly limited. (Invited speakers are of course automatically approved, but need to register anyway.)

Application deadline: 15 July 2017

A minimum stay of one working week is required and we encourage participants to stay for a period of at least two weeks.

There is no registration 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.

Accommodation

Nordita provides rooms for accepted participants free of charge. Most participants will be accommodated at the Stockholm apartment hotel BizApartments, but there are also a few rooms available at Wallquistska Guesthouse, or at Matsällskapet.

Sponsored by:

Monday 4 September

1 Registration / Coffee & Cake

2 Efficiency, power and dissipation of thermal machines

We consider the performance characteristics of thermal engines. Efficiency at maximum power is discussed in a general setting. In particular, it is demonstrated how successive symmetries placed upon the dynamics manifest themselves at the macroscopic level. A general condition is derived under which thermodynamic devices are able to attain a reversible operation. Second, we derive general relations between maximum power, maximum efficiency, and minimum dissipation regimes from linear irreversible thermodynamics.

Speaker: Prof. Bart Cleuren (Hasselt University)

Tuesday 5 September

3 Gym Introduction

4 Experiments on thermodynamics, information, and control using a feedback trap

We report experiments that test aspects of the interplay among thermodynamics, information theory, and control. Our goal is to explore the issues raised historically by Maxwell, Szilard, Landauer, Bennett, which have found renewed interest after the development of stochastic thermodynamics. Our setup consists of a time-dependent, “virtual” double-well potential created by a feedback loop that is much faster than the relaxation time of the particle. Focusing on tests of Landauer’s principle of erasure, we extend Landauer's original scenario to cases where less than a full bit of information is erased. We show experimentally that the appropriate thermodynamic definition of a nonequilibrium system connected to a heat bath is given by the Gibbs-Shannon entropy function, evaluated over nonequilibrium probabilities. We also present preliminary results showing how our setup can be modified to model a combined system for work extraction and measurement.

Speaker: John Bechhoefer (Simon Fraser University)

5 Kettlebell training

Wednesday 6 September

6 Experiments on quantum heat transport in electric circuits

I start by describing how heat currents can be measured in electrical circuits in a low temperature environment. Then I move to two current experiments. The first one is on electronic heat transport through a single-electron transistor, where Wiedemann-Franz law is not obeyed due to Coulomb interaction and quantum processes. The second experiment is on photonic heat transport through a superconducting qubit, where the system acts as an open quantum system with either the qubit-resonator or the resonator-bath coupling acting as the weak coupling.

Speaker: Jukka Pekola (Aalto University)

7 How to detect irreversibility from time-series

If you look at movies of a tracer particle advected by a turbulent flow and its time-reversed version the two movies look very similar, although the system is not in equilibrium but in non-equilibrium stationary state. Can one detect that the system is indeed irreversible from this time series? This curious question has been address by several recent publications who proposed that the irreversibility manifests itself in the following way: the tracer takes long to accelerate but decelerates quickly. This has been quantified by looking at the third moment of two random variables, the power and the increment of energy over a time-scale $\tau$, defined by $W(\tau) = E(t+\tau) - E(t) $. The PDF of both of these random variables are shown to be negatively skewed. Here we extend this result to heavy inertial particles (for example water droplets in atmosphere) who follow a dissipative dynamics. We show that for the heavy inertial particles the same measure of irreversibility works. In addition, we propose a new measure : The PDF of time over which the power keeps the same sign. The tail of such PDFs are found to be exponential hence we can define a characteristic time scale of gain and loss of energy. The characteristic time scale of gain is slow compared to the time scale of loss.

Speaker: Dhrubaditya Mitra

8 Reception

Thursday 7 September

9 Reconstructing surfaces with the Jarzynski relation

Speaker: Dr Astrid de Wijn (NTNU)

10 Kettlebell training

Friday 8 September

11 Time-reversal symmetry and response for systems in a constant external magnetic field

The time-reversal properties of charged systems in a constant external magnetic field are reconsidered, showing that the evolution equations are invariant under novel symmetry operations that imply new signature properties for time-correlation functions under time reversal. Such symmetry relations do not require that the magnetic field be reversed, which makes them applicable to material properties of a single system, rather than of two distinct physical situations. This implies, that Onsager-Casimir relations may be replaced by Onsager reciprocal relations even in the presence of a constant magnetic field, or of mechanically analogous situations. These findings determine, for example, null components of the correlation functions of velocities and currents and of the associated transport coefficients. The theory is developed for both classical and quantum systems, in analogy to Kubo's approach, but the quantum mechanical version leads to new intriguing questions. The theoretical predictions are then illustrated by molecular dynamics simulations of superionic AgI.

Speaker: Prof. Lamberto Rondoni (Politecnico di Torino)

12 Wonders of viscous electronics in graphene [Nordita Seminar]

Speaker: Gregory Falkovich (Weizmann Institute)

Monday 11 September

13 Registration / Coffee & Cake

14 On the value of acquired information in gambling, evolution and thermodynamics

The connection between the information value of a message and capital gain was made by Kelly in 1956. In 1965 Kimura tried to evaluate the rate of information intake by a population undergoing Darwinian evolution by equating it with the substitutional load. Recently, the analogy between Kelly's scheme and work extraction was pointed out in the context of stochastic thermodynamics. I shall try to connect these threads, highlighting analogies and differences between the meaning of information and its value in the different contexts.

Speaker: Prof. Luca Peliti (University "Federico II", Naples)

15 Autonomous thermal motors

We present a minimal model of an autonomous thermal motor, made of two interacting Brownian particles, sitting on two periodic potentials, and kept at different temperatures. We show that such a system does not require ratchet potentials (with, e.g., an asymmetric saw-tooth shape) in order to exhibit direct transport, but presents a spontaneous symmetry breaking. Both the dynamic and thermodynamic properties of the model are discussed. We find that while the model can be solved exactly in the limit of strong coupling between the particles, the optimal operation regime occurs at moderate coupling strength. Furthermore we introduce a model with discrete phase space which captures the essential features of the continuous model and can be solved in the limit of weak coupling.

Speaker: Alberto Imparato (Aarhus University)

Tuesday 12 September

16 On large deviations in non equilibrium systems

Speaker: Bernard Derrida (College de France)

17 Jam Session

18 Kettlebell training

Wednesday 13 September

19 Non equilibrium states with temperature profiles in (1+1)-dimensional Conformal Field Theory

Many one-dimensional quantum systems possess phases with low-energy excitations described by Conformal Field Theory. Examples are carbon nanotubes, quantum Hall edge currents or XXZ spin-chains. Since (1+1)d conformal transformations can map homogeneous systems to nonhomogeneous ones, CFT may be employed to describe certain nonequilibrium situations. I shall discuss how it explains and generalizes the recent results of Langmann-Lebowitz-Mastropietro-Moosavi, Phys. Rev. B 95, 235142 (2017), about the dynamics of states with a preimposed temperature profile in the Luttinger model of 1d electrons.

Speaker: Krzysztof Gawedzki (Laboratoire de Physique, ENS de Lyon FRANCE)

20 Information theoretic analysis of the directional influence between cellular processes

Inferring the directionality of interactions between cellular processes is a major challenge in systems biology. Time-lagged correlations allow to discriminate between alternative models, but they still rely on assumed underlying interactions. Here, we show that an information-theoretic quantity, the transfer entropy (TE), quantifies the directional influence between fluctuating variables in a model-free way. We present a theoretical approach to compute the transfer entropy, even when the noise has an extrinsic component or in the presence of feedback. We re-analyze the experimental data from Kiviet et al. (2014) [1], where fluctuations in gene expression of metabolic enzymes and growth rate have been measured in single cells of Escherichia coli. We confirm the formerly detected modes between growth and gene expression, while prescribing more stringent conditions on the structure of noise sources [2]. Time permitting, I will also present a different project related to the kinetics and thermodynamics of reversible polymerization. More specifically, we are interested in the relaxation dynamics of information carrying polymers undergoing reversible exchange reactions [3]. [1] Stochasticity of metabolism and growth at the single-cell level, D. J. Kiviet et al., Nature, 514, 376 (2014). [2] Information theoretic analysis of the directional influence between cellular processes, S. Lahiri et al., PLOS ONE, under review (2017) [3] Length and sequence relaxation of copolymers under recombination reactions, A. Blokhuis and D. Lacoste, J. Chem. Phys., in press (2017)

Speaker: David Lacoste (ESPCI)

21 Reception

Thursday 14 September

22 Eigenselection and Quantum Thermodynamics

Thermodynamics of nano-sized systems interacting with environments must take into account quantum effects such as system-environment entanglement and environment-induced decoherence, in particular when the coupling with the environments is strong. In a typical thermodynamics scenario, a non-equilibrium system state relaxes to a unique equilibrium state (Gibbs state) whose density matrix is diagonal in the system energy eigenbasis, indicating that coherence among the energy eigenstates is entirely lost. It has been shown that such a kind of decoherence is limited to the weak coupling. When the coupling is strong, the system may reach a steady state where decoherence takes a place in different basis sets. The steady state may not be unique. The situation is even more complicated when the dynamics is not Markovian. Decoherence has been intensively investigated in other fields of physics, namely quantum measurement theory and quantum computing. In the present talk, I will attempt to relate some thermodynamic behaviors, such as relaxation, heat conduction, and heat engine, to such decoherence theory and demonstrate it using non-Markovian open quantum mechanics approach. Some purely quantum effects such as the disappearance of heat conduction due to quantum Zeno effect will be discussed.

Speaker: Ryoichi Kawai (University of Alabama at Birmingham)

23 Kettlebell training

Monday 18 September

24 Registration / Coffee & Cake

25 Infomax Strategies for an Optimal Balance Between Exploration and Exploitation

Proper balance between exploitation and exploration is what makes good decisions that achieve high reward, like payoff or evolutionary fitness. The Infomax principle postulates that maximization of information directs the function of diverse systems, from living systems to artificial neural networks. While specific applications turn out to be successful, the validity of information as a proxy for reward remains unclear. Here, we consider the multi-armed bandit decision problem, which features arms (slot-machines) of unknown probabilities of success and a player trying to maximize cumulative payoff by choosing the sequence of arms to play. We show that an Infomax strategy which optimally gathers information on the highest probability of success among the arms, saturates known optimal bounds and compares favorably to existing policies. Conversely, gathering information on the identity of the best arm in the bandit leads to a strategy that is vastly suboptimal in terms of payoff. The nature of the quantity selected for Infomax acquisition is then crucial for effective tradeoffs between exploration and exploitation.

Speaker: Antonio Celani (ICTP, Quantitative Life Sciences Unit)

Tuesday 19 September

26 Stochastic Chemical Reaction Networks in the Doi-Peliti representation

Models of Chemical Reaction Networks (CRN's) are ubiquitous in several fields. Earlier results identify a class of such networks which have a unique factorized steady-state. For networks not belonging to this class, however, not much is known. We present a general formalism to describe such networks using the Doi-Peliti representation combined with CRN theory, which helps in both deriving a particularly simple representation of the hierarchy of moments, as well as solving them using different techniques. We also comment on Non-equilibrium Work relations in the context of CRN's.

Speaker: Supriya Krishnamurti (SU)

27 Jam Session

28 Kettlebell training

Wednesday 20 September

29 Thermodynamics of Work in Quantum Systems

Definition and measurement of work done on a driven quantum system remains a major challenge in quantum thermodynamics. For closed systems, the standard way to define work is to consider the two-measurement protocol (TMP), where the system is measured at the beginning and end of the drive leading to wave function collapse (loss of quantum coherence) to an energy eigenstate. For open systems, the stochastic mapping to the Lindblad master equation and its unraveling by quantum jumps offers a powerful way to define and calculate thermodynamics of work and the related fluctuation relations within the TMP [1]. However, for quantum systems with coherence it has recently been shown that it is impossible to define a work operator that satisfies proper physical requirements (the "no-go" theorem) [2]. To this end, we propose a novel way to define work based on the Hamilton-Jacobi formulation of quantum mechanics, which allows to define phase space trajectories with well-defined energy for any wave function [3]. We illustrate this approach by explicit calculations for a driven quantum harmonic oscillator. 1. S. Suomela, J. Salmilehto, I.G. Savenko, T. Ala-Nissila, and M. Mottonen, Phys. Rev. E 91, 022126 (2016). 2. M. Perarnau-Llobet, E. Baumer, K.V. Hovhannisyan, M. Huber, and A. Acin, Phys. Rev. Lett. 118, 070601 (2017). 3. R. Sampaio, S. Suomela, T. Ala-Nissila, J. Anders, and Th. Philbin, https://arxiv.org/abs/1707.06159(2017).

Speaker: Prof. Tapio Ala-Nissilä (Aalto University, Finland, and Loughborough University, UK)

30 Generic properties of stochastic entropy production

Entropy production is a central quantity in stochastic thermodynamics, satisfying the fluctuation relations under very general conditions. Recently, new (and surprising) generic properties of entropy production have been discovered, such as uncertainty inequalities and the "infimum law". It is unclear if there are even more generic properties of entropy production, and how these properties are related. In this talk, I will present a general theory for non-equilibrium physical systems described by overdamped Langevin equations. For these system, entropy production evolves according to a simple stochastic differential equation, which depends on the underlying physical model. However, at steady state, a random time transformation maps this evolution into a model-independent form. This implies several generic properties for the entropy production, such as a finite-time uncertainty equality, universal distributions of the infimum and the supremum before the infimum, and universal distribution of the number of zero-crossings. I will conclude with generalizing some of the results to systems out of steady state. Ref. Pigolotti, Neri, Roldán, Jülicher, under revision (arXiv:1704.04061).

Speaker: Simone Pigolotti (Okinawa Institute of Science and Technology (OIST))

31 Reception

Thursday 21 September

32 Thermodynamics and Information at the nanoscale

Thermodynamic laws have been key for the design of useful everyday devices from car engines and fridges to power plants and solar cells. Technology’s continuing miniaturisation to the nanoscale is expected to soon enter regimes where standard thermodynamic laws do not apply. I will give an introduction to quantum thermodynamics - the emerging research field that aims to uncover the thermodynamic laws that govern small ensembles of systems that follow non-equilibrium dynamics and can host quantum properties [1]. I will discuss a nanoscale thermodynamic experiment with heated optically trapped nanospheres in a dilute gas [2]. By developing a new theoretical model that captures the non-equilibrium situation of the particles, we were able to measure the surface temperature of the trapped spheres and observe temperature gradients on the nanoscale. In the second part of the talk I will discuss recent theoretical advances in defining thermodynamic work in the quantum regime. By introducing a process that removes quantum coherences we were able to show that work cannot only be extracted from classical non-equilibrium systems, additional work can be extracted from quantum coherences [3]. [1] Quantum thermodynamics, S. Vinjanampathy, J. Anders, Contemporary Physics 57, 545 (2016). [2] Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere, J. Millen, T. Deesuwan, P. Barker, J. Anders, Nature Nanotechnology 9, 425 (2014). [3] Coherence and measurement in quantum thermodynamics, P. Kammerlander, J. Anders, Scientific Reports 6, 22174 (2016).

Speaker: Janet Anders (University of Exeter)

17:00 Kettlebell training

Friday 22 September

33 Thermodynamic structures in adaptation and evolution of growing populations

Fitness, defined by the long-term growth of a population, is the central quantity that characterizes the evolutionary success of the population macroscopically. The innovations of single-cell imaging and long-term tracking techniques have revealed a huge heterogeneities in populations of cells, and also enabled us to investigate how microscopic behaviors of the single cells are linked to the macroscopic properties of the population, including fitness. In addition, it has been revealed that the problem of the adaptation and evolution of growing populations shares a lot with the information thermodynamics and the steady state thermodynamics, suggesting that we can use the knowledge in these fields for understanding the evolution. In this talk, I attempt to outline how the problems of evolution and thermodynamics are related. By highlight their similarities and differences, I am going to show the open problems and challenges in the evolution and adaptation at the cellular level.

Speaker: Tetsuya Kobayashi (University of Tokio, Institute of Industrial Science)

Monday 25 September

09:00 Registration / Coffee & Cake

34 Linear and non-linear thermodynamics of a kinetic heat engine with fast transformations

We investigate a kinetic heat engine model constituted by particles enclosed in a box where one side acts as a thermostat and the opposite side is a piston exerting a given pressure. Pressure and temperature are varied in a cyclical protocol of period $\tau$ and their relative excursions $\delta$ and $\epsilon$ respectively, constitute the thermodynamic forces dragging the system out-of-equilibrium. The analysis of the entropy production of the system allows to define the conjugated fluxes, which are proportional to the extracted work and the consumed heat. The dynamics of the piston can be approximated, through a coarse-graining procedure, by a Klein-Kramers equation which - in the linear regime - yields analytic expressions for the Onsager coefficients and the entropy production. A study of the efficiency at maximum power shows that the Curzon- Ahlborn formula is always an upper limit which is approached at increasing values of the thermodynamic forces, i.e. outside of the linear regime.

Speaker: Prof. Angelo Vulpiani (Dipartimento di Fisica, Universita' Sapienza)

35 A protocol for reaching equilibrium arbitrary fast

When a control parameter of a system is suddenly changed, the accessible phase space changes too and the system needs its characteristic relaxation time to reach the final equilibrium distribution. An important and relevant question is whether it is possible to travel from an equilibrium state to another in an arbitrary time, much shorter than the natural relaxation time. Such strategies are reminiscent of those worked out in the recent field of Shortcut to Adiabaticity, that aim at developing protocols, both in quantum and in classical regimes, allowing the system to move as fast as possible from one equilibrium position to a new one, provided that there exist an adiabatic transformation relating the two. Proof of principle experiments have been carried out for isolated systems. Instead in open system the reduction of the relaxation time, which is frequently desired and necessary, is often obtained by complex feedback processes. In this talk, we present a protocol,named Engineered Swift Equilibration (ESE), that shortcuts time-consuming relaxations, We tested experimentally this protocol on a Brownian particle trapped in an optical potential first and then on an AFM cantilever. We show that applying a specific driving, one can reach equilibrium in an arbitrary short time. We also estimate the energetic cost to get such a time reduction. Beyond its fundamental interest, the ESE method paves the way for applications in micro and nano devices, in high speed AFM, or in monitoring mesoscopic chemical or biological process. References: (1) Engineered Swift Equilibration, Ignacio A Martinez; Artyom Petrosyan; David GuŽry-Odelin; Emmanuel Trizac; Sergio Ciliberto, Nature Physics, Vol 12, 843 (2016). (2) Arbitrary fast modulation of an atomic force microscope, Anne Le Cunuder; Ignacio A Martinez; Artyom Petrosyan; David Gury-Odelin; Emmanuel Trizac; Sergio Ciliberto. Applied Physics Letters, 109, 113502 (2016)

Speaker: Prof. Sergio Ciliberto (ENS-Lyon)

Tuesday 26 September

36 The thermodynamic uncertainty relation

The thermodynamic uncertainty relation conjectured in 2015 [1] and proven using large deviation theory in 2016 [2] provides a universal constraint relating mean and dispersion of any current in a driven system with the overall entropy production. I will first introduce the basic concepts behind this relation and then discuss a few of its applications. Prominent amomg those are a universal model-free bound on the efficiency of molecular motors [3] and insight into the current debate whether or not heat engines can approach Carnot efficiency at finite power [4]. Stronger versions of this bound require knowledge of the underlying topology and driving affinities of the network [5]. [1] A. C. Barato and U.S., Phys. Rev. Lett. 114, 158101, 2015 [2] T. R. Gingrich, et al, Phys. Rev. Lett. 116, 120601, 2016 [3] P. Pietzonka, A. C. Barato, and U.S., J. Stat. Mech., 124004, 2016 [4] P. Pietzonka and U.S., arxiv 1705.05817. [5] P. Pietzonka, A. C. Barato, and U. Seifert J Phys A, 49, 34LT01, 2016

Speaker: Udo Seifert (University of Stuttgart)

Jam Session

37 Kettlebell training

Wednesday 27 September

38 Tracer particles in two-dimensional elastic networks diffuse logarithmically slow

I will discuss the long time asymptotic behavior of a tagged particle in systems where the particles are stuck with their neighbors. In one dimension this corresponds to single-file diffusion, where the mean squared displacement of a particle grows with the square root of time. In two dimensions it turns out that the mean square displacement grows logarithmically, and above two dimensions the motion of the particle is bounded. I will show how one can arrive at these results through an approach called harmonization.

Speaker: Prof. Michael Lomholt (University of Southern Denmark)

39 Stochastic thermodynamics with a time-dependent system-bath coupling

Stochastic thermodynamics in Sekimoto's formulation is based on a division of the world into three parts: the System, the External System, which can influence the System by modifying the System's potential energy, and the Bath. Usually the system-bath coupling is taken constant, but one could also imagine that this depends explicity on time. Does such a change lead to heat or change in internal energy (or both)? I will discuss such issues and the motivation which led me to it, problems in an approach to quantum heat.

Speaker: Prof. Erik Aurell (KTH)

Thursday 28 September

17:00 Kettlebell training