"Current and Future Trends in Stochastic Thermodynamics" chaired by
Ralf Eichhorn (Nordita)
, Erik Aurell (KTH)
, Astrid de Wijn (Stockholm University)
, Bart Cleuren (Hasselt University)

from Monday 04 September 2017
(09:00)
to Friday 29 September 2017
(18:00)
at
Nordita, Stockholm
(
122:026
)

Description:

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.

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.

Efficiency, power and dissipation of thermal machines (1h00')

Bart Cleuren (Hasselt University)

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.

Experiments on thermodynamics, information, and control using a feedback trap (1h00')

John Bechhoefer (Simon Fraser University)

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.

Experiments on quantum heat transport in electric circuits (1h00')

Jukka Pekola (Aalto University)

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.

14:00

How to detect irreversibility from time-series (1h00')

Dhrubaditya Mitra

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.

Time-reversal symmetry and response for systems in a constant external magnetic field (1h00')

Lamberto Rondoni (Politecnico di Torino)

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.

16:15

Wonders of viscous electronics in graphene [Nordita Seminar] (1h00')
(Location:
Albanova
(
FA32
)
)

On the value of acquired information in gambling, evolution and thermodynamics (1h00')

Luca Peliti (University "Federico II", Naples)

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.

14:00

Autonomous thermal motors (1h00')

Alberto Imparato (Aarhus University)

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.

Non equilibrium states with temperature profiles in (1+1)-dimensional Conformal Field Theory (1h00')

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

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.

14:00

Information theoretic analysis of the directional influence between cellular processes (1h00')

David Lacoste (ESPCI)

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)

Ryoichi Kawai (University of Alabama at Birmingham)

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.

Infomax Strategies for an Optimal Balance Between Exploration and Exploitation (1h00')

Antonio Celani (ICTP, Quantitative Life Sciences Unit)

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.

Stochastic Chemical Reaction Networks in the Doi-Peliti representation (1h00')

Supriya Krishnamurti (SU)

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.

Tapio Ala-Nissilä (Aalto University, Finland, and Loughborough University, UK)

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).

14:00

Generic properties of stochastic entropy production (1h00')

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

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).

Thermodynamics and Information at the nanoscale (1h00')

Janet Anders (University of Exeter)

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).

Thermodynamic structures in adaptation and evolution of growing populations (1h00')

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

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.

Linear and non-linear thermodynamics of a kinetic heat engine with fast transformations (1h00')

Angelo Vulpiani (Dipartimento di Fisica, Universita' Sapienza)

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.

14:00

A protocol for reaching equilibrium arbitrary fast (1h00')

Sergio Ciliberto (ENS-Lyon)

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 Gury-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)

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

Tracer particles in two-dimensional elastic networks diffuse logarithmically slow (1h00')

Michael Lomholt (University of Southern Denmark)

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.

14:00

Stochastic thermodynamics with a time-dependent system-bath coupling (1h00')

Erik Aurell (KTH)

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.