Measuring and Manipulating Non-Equilibrium Systems

14 Oct 2024, 09:00 → 25 Oct 2024, 18:00 Europe/Stockholm

Albano 3: 6203 - Floor 6 Large Lunch Room (44 seats) (Albano Building 3)

Astrid de Wijn (Stockholm University and NTNU), Bart Cleuren (Hasselt University), Ralf Eichhorn (Stockholm University, Nordita), Supriya Krishnamurthy (Stockholm University)

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Venue

Nordita, Stockholm, Sweden

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Background

Equilibrium statistical physics provides an extremely powerful and universal formalism for describing the behaviour of many-particle systems in thermal equilibrium, but we have no counterpart of such a theory for non-equilibrium systems. Since most systems and processes found in nature are out of equilibrium, such a theory, if it can be formulated, will have an enormous impact. Indeed the large interest in the field of Stochastic Thermodynamics stems from the fact that, under certain restrictions and assumptions, it provides a general theory for small out-of-equilibrium systems which generalizes fundamental equilibrium concepts such as the fluctuation-dissipation theorem, current fluctuations and linear response to the non-equilibrium domain.

Currently the interest of the statistical physics community is divided broadly into expanding the field of stochastic thermodynamics to encompass an even larger class of systems, as well as to understand costs, trade-offs and constraints in the process of measuring or manipulating non-equilibrium systems. An understanding of these issues could definitely lead to many applications but also to new insights into non-equilibrium behaviour. In this program we aim to discuss these topics.

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Confirmed speakers

Janet Anders	Satya Majumdar
Debra Bernhard	Patrick Pietzonka
Stefano Bo	Lamberto Rondoni
Sergio Ciliberto	Udo Seifert
Lennart Dabelow	Janine Splettstößer
Salambô Dago	Shoichi Toyabe
Sabine Klapp	Gatien Verley
Christian Maes	Tan Van Vu
Sreekanth Manikandan

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Setup

This program aims at discussing the latest developments and open problems in understanding the fundamental costs, constraints and trade-offs which characterize the thermodynamic behavior of non-equilibrium systems. It is set up in a casual and informal way with two (maximal three) presentations scheduled per day (probably in the morning, about 60 min each). In that way, there will be ample time for discussions and for working on particular questions that may arise during the course of the program.

Registration

Registration is open now! Deadline: Aug 31, 2024

To apply for participation in 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.

We have a limited amount of funds available, which we will mainly use for providing accommodation for participants. However, we unfortunately cannot guarantee to provide free accommodation to all participants. We thus kindly ask you to cover travel expenses yourself, and contact the organizers about possible travel support only if this is completely impossible.

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Sponsored by:

Monday 14 October

09:30 Welcome breakfast

1 The induced friction on a probe moving in a nonequilibrium medium

Using a powerful combination of projection-operator method and path-space response theory, we derive the fluctuation dynamics of a slow inertial probe coupled to a steady nonequilibrium medium under the assumption of time-scale separation. The nonequilibrium is realized by external nongradient driving on the medium particles or by their (athermal) active self-propulsion. The resulting friction on the probe is an explicit time-correlation for medium observables and is decomposed into two terms, one entropic proportional to the noise variance as in the Einstein relation for equilibrium media, and a frenetic term that can take both signs. As illustration, we give the exact expressions for the friction and noise of a probe in a rotating run-and-tumble medium.  We find a transition to absolute negative probe friction as the nonequilibrium medium exhibits sufficient and persistent rotational current.  There, the run-away of the probe to high speeds realizes a nonequilibrium-induced acceleration.  Simulations show that its speed finally saturates, yielding a symmetric stationary probe-momentum distribution with two peaks.

Speaker: Christian Maes (KU Leuven)

Tuesday 15 October

2 Experimental implementation of optimal transport and efficient control in thermal systems

This talk focuses on two distinct but related experiments in thermal systems. The first is an experimental demonstration of optimal transport in thermal systems using a microscopic particle trapped by optical tweezers. In particular, we achieve the optimal transport of translation and Landauer erasure that reaches the finite-speed thermodynamic minimum of the entropy production. The second is the experimental exploration of the efficient control of a single-molecule molecular motor F1-ATPase. This motor is forcedly rotated in cells to generate ATP molecules. However, it remains unclear how the motor is rotated. To partially answer this question, we experimentally compare the work necessary to rotate the motor by different torque modes. The results highlight the importance of suppressing nonequilibrium fluctuations for efficient control.

Speaker: Shoichi Toyabe (Tohoku University)

3 Time-cost-error trade-off relation in thermodynamics: The third law and beyond

The unattainability principle of the third law of thermodynamics states that it is impossible to bring a system to its ground state within a finite number of steps. This no-go principle has been rigorously proven in a general setup, and several bounds on the achievable error in terms of reservoir parameters have been derived in the literature. However, the quantitative relationship between the error and crucial resources, such as time and energetic cost, remains elusive. Moreover, there is a strong desire to generalize and quantify this principle as a unifying characteristic across diverse thermodynamic operations beyond the task of cooling.

In this talk, we present a resolution to the above problem. To this end, we introduce the concept of "separated states," where all states are classified into two distinct categories: desired states and undesired states. This notion not only encompasses the traditional third law but also significantly broadens its applicability to a wide range of thermodynamic processes, including information erasure, copying, and biological processes such as proofreading. Within a general setup, we derive a three-way trade-off relation that connects the operational time, energetic cost, and attainable error associated with achieving separated states. This relation rigorously quantifies the principle that as thermodynamic operations approach absolute precision, they inevitably require either infinite operation time or infinite thermodynamic cost. Our results represent a significant generalization of the unattainability principle, central to the third law, and offer a fresh perspective on thermodynamic limitations. Lastly, we address several open questions in this direction.

Speaker: Tan Van Vu (Yukawa Institute for Theoretical Physics, Kyoto University)

4 Some results on measurement-induced stochastic dynamics of a single qbit

Speaker: Abhishek Dhar (International Centre for Theoretical Sciences, TIFR, Bengaluru)

NORDITA2024.pdf

Wednesday 16 October

5 Exact & non-exact response theory from nonequilibrium molecular dynamics to stochastics

The Fluctuation Relation derived by Evans, Cohen and Morriss in 1993 has eventually led to a general theory of response that is exact, and not limited to small perturbations. This theory arising in the field of deterministic dynamics, nonequilibrium molecular dynamics in particular, has been recently extended to stochastic perturbations. We investigate some pedagogical example, that includes systems in extreme conditions as well as systems undergoing phase transitions, highlighting the difference between linear response and exact response.

Speaker: Lamberto Rondoni (Politecnico di Torino)

Stockholm16102024.pdf

6 Understanding non-equilibrium steady states using deterministic dynamics

Speaker: Debra Bernhardt (The University of Queensland)

18:00 Dinner

Thursday 17 October

7 Irreversibility at dynamical transitions of feedback-driven and non-reciprocal systems

This talk centers around the question to which extent measures of irreversibility in a nonequilibrium system serve as a signal of changes (transitions) in the dynamical behavior. We consider two examples. The first involves a single particle driven by repulsive time-delayed feedback. Recently it has been shown that this type of feedback can lead to persistent motion above a threshold in parameter space. We investigate, numerically and by analytical methods, the rate of heat production in the different regimes around the threshold to persistent motion. As function of delay time, the heat production rate shows a pronounced maximum close above the onset of persistent motion, whereas other parameter dependencies show no marked behavior. The distribution of dissipated heat is non-Gaussian at both sides of the transition.

The second example involves a many-particle system of active particles with non-reciprocal polar interactions. At strong coupling conditions, the system shows complex dynamical phase behavior that, on a hydrodynamic level, is characterized by exceptional points. We discuss consequences for the rate of entropy production on the particle level.

Speaker: Sabnine Klapp (Technical University Berlin, Institute for Theoretical Physics)

8 Single-molecule trajectories in chemically active condensates

The components of cells need to be organised and separated. Sometimes, this is done with physical membranes. But more recently, it's been discovered that the machinery and contents of cells can be separated from the surrounding environment like drops of oil separate from water -- we call these compartments biomolecular condensates. The diffusive dynamics and chemical kinetics of individual molecules inside condensates can be studied experimentally by fluorescent labelling, offering key insights into subcellular dynamics. I will discuss how biomolecular condensates govern the kinetics of chemical reactions and how this is reflected in the dynamics of labelled molecules. This will allow me to discuss how the physics of phase separation influences the evolution of single-molecule trajectories and governs their statistics. I will show that, out of equilibrium, the interactions leading to phase separation induce systematic directed motion at the level of single molecules and enhance diffusion. I will then present how we can use stochastic thermodynamics to quantify how far from equilibrium condensates are.

Speaker: Stefano Bo (King's College London)

9 Kinetic bounds for nonequilibrium systems

Speaker: Marco Baiesi (University of Padova)

Baiesi_Nordita_2024.pdf

Friday 18 October

10 Extreme-temperature single-particle heat engine

Thermodynamics at the micro-scale exhibits distinctive features due to the fluctuating exchange of energy between small objects and their environment. This regime of stochastic thermodynamics explains many cellular and biological processes, and a full understanding is required in the development of nanotechnologies. We present an experiment underdamped single-particle heat engine, where weak coupling to the thermal environment enables us to define synthetic heat baths with temperatures in excess of 10^5 K. Such an engine has an efficiency of over 10%, and exhibits many unique features of this thermodynamic regime, including giant efficiency fluctuations and breaking of the equipartition theorem

Speaker: Janet Anders (University of Exeter & University of Potsdam)

11 A bottom-up approach for circuits of thermodynamics converters

In this presentation, I will develop a general framework for thermodynamic circuits operating in stationary nonequilibrium. I will assume a decomposition of the circuit into several sub-devices with well-defined non-equilibrium conductances (scalar functions of thermodynamic forces for dipoles, Onsager response matrices for linear multipoles, or their non-linear extension called nonequilibrium conductance matrices [1]). I will consider two paradigmatic types of associations (serial and parallel) to assemble the sub-devices and determine, through successive pairwise associations, the equivalent conductance of the circuit [2]. The resulting conductance provides the global current-force characteristic of the circuit, and also some bounds on the covariance of currents (in connection with Thermodynamic Uncertainty Relations). Conservation laws play a crucial role and shall be determined throughout the association process, either inside associated sub-devices or at their interfaces. In the latter case, the circuit complexity reappears in the mixed boundary conditions of its sub-parts. While this work lays the foundation for further studies on thermodynamic circuits, with applications ranging from thermoelectric systems [3] to chemical reaction networks (CRN), many questions remain open: Can one actually measure the nonlinear conductance of a thermodynamic converter? How can the multistability of circuits be tackled? Is the working point of a circuit determined by an extremization principle? Can this approach be computationally useful for large CRNs?

[1] H. Vroylandt, D. Lacoste, and G. Verley, “Degree of coupling and efficiency of energy converters far-from-equilibrium,” J. Stat. Mech: Theory Exp., 2018
[2] P. Raux, C. Goupil, and G. Verley, “Thermodynamic circuits: Association of devices in stationary nonequilibrium,” Phys. Rev. E, vol. 110, no. 1, p. 14134
[3] P. Raux, C. Goupil, and G. Verley, “Thermodynamic Circuits 2: Nonequilibrium conductance matrix for a thermoelectric converter,” Arxiv, May 2024

Speaker: Gatien Verley (Université Paris Saclay)

Monday 21 October

12 Stochastic Resetting

In this talk, I aim to give a pedagogical overview of the rapidly developing field of `stochastic resetting', relevant in many fields that typically involve a random searchprocess. Stochastic resetting simply means interrupting the natural dynamics of a system at

random times and reset the system back to its initial condition. This resetting move breaks detailed balance and drives the system into a nonequilibrium stationary state. The approach to the stationary state is accompanied by an unusual ‘dynamical phase transition’. Moreover, the mean first-passage time to a fixed target becomes a minimum at an optimal value of the resetting rate. This makes the diffusive search process more efficient. Recent experiments in optical traps have verified some of the theoretical predictions, but also have raised new interesting questions. Going beyond the classical regime, there have been recent developments in quantum resetting also. I hope to explain why stochastic resetting has emerged in recent years as an exciting field of research in nonequilibrium statistical
physics.

Speaker: Satya Majumdar (CNRS, LPTMS, Universite Paris-Saclay)

reset_Stockholm_2024.pdf

13 Thermodynamic nature of irreversibility in active matter

Active matter describes systems whose constituents can convert energy from their surroundings into directed motion, such as bacteria or colloids with catalytic surfaces. For similar passive systems, the second law and more recent fluctuation theorems relate the irreversibility of their dynamics to the thermodynamic entropy production. Crucially, "irreversibility" is a purely dynamical measure, the log-ratio of the probabilities to observe a given trajectory and its time reverse, while "entropy" is thermodynamically related to the

dissipated heat via Sekimoto's stochastic energetics. We reveal a similar link between the dynamics and thermodynamics for suspensions of interacting active particles at sufficiently low density: The irreversibility is a state function of the thermodynamic system parameters, namely the volume, the temperature, and the so-called active or swim pressure.

Speaker: Lennart Dabelow (Queen Mary University of London)

presentation.pdf

Tuesday 22 October

14 Measurement based manipulation of nano-systems under stochastic noise : An introduction to Feedback control.

When dealing with nano-systems whose dynamics are governed by thermal (or quantum) fluctuations, feedback schemes (measuring and applying forces accordingly) represent a powerful tool for manipulating them. In this talk, we will discuss two experimental applications of feedback control and explore fundamental physics through the resulting non-equilibrium steady states.

First, we demonstrate how a feedback loop can create a virtual double potential for an underdamped micro-mechanical oscillator, which can be used as a 1-bit memory. This platform is employed to implement fast, and therefore out-of-equilibrium, 1-bit logical operations and to study the energetic cost of information processing in the underdamped regime [1,2,3]. How is thermodynamics modified when the underdamped system doesn’t equilibrate with the bath at all times? When should the feedback be considered as a daemon pumping information?
In the second part, we address a novel use of feedback for quantum control of nanospheres in optical traps, going beyond the state-of-the-art feedback cooling to the motional ground state [4]. We propose an original approach that uses feedback to maintain the particle in the dark spot (the intensity minimum, which avoids internal heating due to absorption) of a higher laser mode (e.g., the tip of a double-well potential) while still enabling optimal optical displacement measurement (in combination with Kalman filters to optimally estimate the full quantum state). We demonstrate levitation in the dark configuration in an experimental double-well setup without the need for any confining potential in 1D. The FLIP (Feedback Stabilization on an Inverted Potential) method overcomes the absorption limitations of standard optical levitation but also raises fundamental questions. Unlike the harmonic potential in standard optical traps, the equilibrium point in FLIP is unstable, meaning active feedback is required to keep the particle in the dark. We investigate the optimal feedback cost function to reach a pure state at the inverted position and discuss the resulting steady state, which is only defined under continuous measurement and feedback.

[1] S. Dago, J. Pereda, S. Ciliberto, and L. Bellon. Virtual double-well potential for an underdamped oscillator created by a feedback loop. Journal of Statistical Theory and Experiment, 2022(5):053209, May 2022.
[2] S. Dago, J. Pereda, N. Barros, S. Ciliberto, and L. Bellon. Information and thermodynamics: Fast and precise approach to landauer’s bound in an underdamped micromechanical oscillator. Phys. Rev. Lett., 126:170601, 2021.
[3] S. Dago, L. Bellon. Logical and thermodynamical reversibility: optimized experimental implementation of the not operation. Phys. Rev. E 108, L022101 ,August 2023
[4] L. Magrini, P. Rosenzweig, C. Bach, A. Deutschmann-Olek, S. G. Hofer, S. Hong, N. Kiesel, A. Kugi, and M. Aspelmeyer. Real-time optimal quantum control of mechanical motion at room temperature. Nature 595, 373 (2021).

Speaker: Salambô Dago (University of Vienna)

15 Inertial effects in discrete sampling information engines

We describe an experiment on an underdamped mechanical oscillator used as an information engine. The system is equivalent to an inertial Brownian particle confined in a harmonic potential whose center is controlled by a feedback protocol which measures the particle position at a specific sampling frequency $$1/\tau$$ . Several feedback protocols are applied and the power generated by the engine is measured as a function of the oscillator parameters and the sampling frequency. The optimal parameters are then determined. The results are compared to the theoretical predictions and numerical simulations on overdamped systems. We highlight the specific effects of inertia, which can be used to increase the amount of power extracted by the engine. In the regime of large $$\tau$$, we show that the produced work has a tight bound determined by information theories.

Speaker: Sergio Ciliberto (ENSL and CNRS)

Wednesday 23 October

16 Inference and localization of entropy production beyond the thermodynamic uncertainty relation

Entropy production arguably is the most universal quantifier for non-equilibrium systems in contact with a thermal bath of well-defined temperature. If not all driven degrees of freedom are accessible, it can typically not be inferred exactly from experimental data. One goal of thermodynamic inference is to derive at least a model-free lower bound from such data. The thermodynamic uncertainty relation with its generalization to time-dependent driving is the most prominent example to date as I will first recall in this talk. Even better bounds can be achieved by using waiting-time distributions and the novel concepts of Markovian events and Markovian snippets that allow a thermodynamically consistent identification of entropy production along individual coarse-grained trajectories [1-3]. As an illustration I will show an application to experimental data on unfolding of a small peptide [4].

[1] J. van der Meer, B. Ertel, and U. Seifert, PRX 12, 031025, 2022
[2] J. van der Meer, J. Degünther, and U. Seifert, PRL 130, 257101, 2023
[3] J. Degünther, J. van der Meer, and U. Seifert, PRR 6, 023175, 2024
[4] J. Degünther, J. van der Meer, and U. Seifert, PNAS 121, e2405371121, 2024

Speaker: Udo Seifert (Univ Stuttgart)

stockholm24.pdf

17 Fluctuation theorems and bounds for nonequilibrium nanoscale engines

Energy conversion processes in nanoscale devices are potentially strongly impacted by fluctuations. It is therefore of high interest to understand if and how these fluctuations are related to the desired outcome of the process. While in systems close to equilibrium, fluctuation-dissipation theorems exist, relating the fluctuations to the average response of the system, such relations are typically harder to find in nonequilibrium situations. More general fluctuation relations, holding also in nonequilibrium, are at the basis of recently studied bounds on the fluctuations such as the so-called thermodynamic uncertainty relation. These are however typically applicable mostly to classical or weakly coupled systems.

In this talk I will present recent progress in establishing constraints on the fluctuations in nonequilibrium, possibly strongly coupled systems. These results are obtained from scattering theory, which applies to a large class of systems, as long as particle-particle interactions are weak. For nanoscale heat engines, possible subject to a large temperature bias, we find a bound on the power fluctuations given by the power itself, which holds even when the thermodynamic uncertainty relation breaks down [1]. Furthermore, we prove a sort of kinetic uncertainty relation for quantum transport of particles, energy or entropy, which in the classical limit bounds the precision by the “activity” of the system - independently of whether the system is bosonic or fermionic and even when the contacts are nonthermal [2]. In the quantum regimes, these kinetic uncertainty relations need to be modified, where the quantum statistics (fermionic/bosonic) play an important role for the validity and shape of these bounds.

[1] L. Tesser, J. Splettstoesser: Out-of-Equilibrium Fluctuation-Dissipation Bounds. Phys. Rev. Lett. 132, 186304 (2024)
[2] D. Palmqvist, L. Tesser, J. Splettstoesser: Quantum kinetic uncertainty relations, in preparation.

Speaker: Janine Splettstößer (Chalmers)

slides_splett.pdf

18:00 Dinner

Thursday 24 October

18 Bounds on entropy production by measuring the timing of events

I will discuss recent work on universal bounds on entropy production that relate to the periodicity of a measured signal of discrete events of an otherwise hidden non-equilibrium system. The trade-off between cost and precision is expressed by non-linear mathematical functions, which vary slightly depending on the choice for the measure of precision and the time-symmetry of the observable. The bounds can be saturated for optimally designed Markov networks. The thermodynamic uncertainty relation, which applies to current-like observables, is thereby complemented for the general class of counting observables.

As an outlook towards possible future directions of the field, I will speculate how similar non-linear trade-offs between cost and precision could play a role for general models of clocks.

Speaker: Patrick Pietzonka (University of Edinburgh)

19 Inference and Control of Cellular Processes

Quantifying the spatiotemporal forces, affinities, and dissipative costs of cellular processes from experimental data, developing coarse-grained models to capture experimental observations, and leveraging those to target specific processes or features through external control remain significant challenges. Here, I explore how principles from stochastic thermodynamics, combined with machine learning techniques, offer a promising approach to addressing these issues. We present preliminary results from experiments on fluctuating cell membranes and simulations of the self-assembly of branched actin networks, as well as kinesin-mediated cargo transport along intracellular tracks. These studies suggest potential avenues for non-equilibrium inference and control in experimental biophysical contexts, and highlights the complexities and limitations that still need to be addressed.

Speaker: Sreekanth Manikandan (Stanford University)

20 Entropy and work in stochastic resetting processes

Speaker: Kristian Stølevik Olsen (Heinrich Heine University Düsseldorf)

Friday 25 October

09:30 Goodbye Breakfast

21 Concluding discussions (self-organized)