Tuesday, 14 June 2022

Progressive quenching (PQ) is a controlled update of the partition between a system and its external system. More precisely, we take an Ising spin system on a complete lattice, and we quench one after another the thermally fluctuating spins evolving by a Markovian dynamics. The individual realizations show a persistent memory, which can be characterised by a martingale process of the mean of the unquenched spins. We can derive a variety of aspects from this martingale that go beyond simple conditional expectation. They reflect an extended canonical structure that underlies QP.

In many physical systems, we are faced with an interaction between mechanisms that evolve at very different time scales. In this seminar, we will consider Markovian processes with such characteristics, and we will exploit the time scale separation to obtain an effective Markovian dynamics on a reduced state space. In particular, compared to existing studies, we will introduce a more general formalism.

Finally, as a privileged example, we consider the limit of the strong continuous measure of quantum systems described by a quantum trajectory with Gaussian noise.

Landauer's bound is the minimum thermodynamic cost for erasing one bit of information. As this bound is achievable only for quasistatic processes, finite-time operation incurs additional energetic costs. We find a “tight” finite-time Landauer's bound by establishing a general form of the classical speed limit. This tight bound well captures the divergent behavior associated with the additional cost of a highly irreversible process, which scales differently from a nearly irreversible process. We demonstrate the validity of this bound via discrete one-bit and coarse-grained bit systems. Our work implies that more heat dissipation than expected occurs during high-speed irreversible computation.

Ref: J. S. Lee, S. Lee, H. Kwon, and H. Park, arXiv:2204.07388

Thermodynamic inference aims at revealing hidden properties of non-equilibrium systems by using universal results from stochastic thermodynamics. One key quantity of such systems is their entropy production, which is hard to get exactly without having full access to the system. Universal lower bounds can be derived by various types of coarse-graining and optimization approaches. A particularly promising tools is the thermodynamic uncertainty relation (TUR), which, inter alia, yields a model-free lower bound on the efficiency of molecular motors as I will show using experimental data for kinesin. Inference from waiting-time distributions between consecutive transitions yields further information about topological aspects of the underlying network. For coherent oscillations, I will present a conjecture on their universal minimal cost.

A fundamental feature of nonequilibrium processes is that they are governed by a trade-off between dissipation, speed, and uncertainty. We show how to quantify this nonequilibrium trade-off with first-passage quantities, and subsequently, we discuss distinct advantages of the first-passage approach. We also relate the derived trade-off relations to the van’t Hoff-Arrhenius law that holds for processes near equilibrium. As an application, we estimate the rate of dissipation in a nonequilibrium process from repeated realisations of a first-passage process, and we compare the first-passage approach with alternative approaches based on the thermodynamic uncertainty ratio and the Kullback-Leibler divergence.

We study the stochastic thermodynamics of cell growth and division using a theoretical framework based on branching processes with resetting. Cell division may be split into two sub-processes: branching, by which a given cell gives birth to an identical copy of itself, and resetting, by which some properties of the daughter cells (such as their size or age) are reset to new values following division. We derive the first and second laws of stochastic thermodynamics for this process, and identify separate contributions due to branching and resetting. We apply our framework to well-known models of cell size control, such as the sizer, the timer, and the adder. We show that the entropy production of resetting is negative and that of branching is positive for these models in the regime of exponential growth of the colony. This property suggests an analogy between our model for cell growth and division and heat engines, and the introduction of a thermodynamic efficiency, which quantifies the conversion of one form of entropy production to another.

[1] Genthon et al., J. Phys. A.: Math. Theor. 55, 074001 (2022)

Wednesday, 15 June 2022

Boltzmann’s explanation of irreversibility is based on the concept of macro-states and the definition of entropy as the logarithm of the volume in phase space of the region of micro-states compatible with a given macro-state. The explanation, however, lacks an objective (i.e. non arbitrary) definition of macro-states and of the crossover between micro- and macro-scales. Here we show that this problem can be solved by reformulating Boltzmann’s explanation in terms of observables relaxing from giant fluctuations. We show that the irreversible behavior of an observable is a fully objective property and has nothing to do with its micro- or macroscopic nature. In fact, we will show a situation where a system exhibits irreversibility at the micro-scale and reversibility at the macro-scale. In the second part of the talk, we propose a mechanism for creating giant fluctuations of an observable (hence, irreversibility) based on metastable states induced by symmetry breaking.

(Passive) Brownian heat engines are popular systems where a single microscopic particle is confined with the help of an optical trap and cycled through a time dependent protocol and kept in contact with two heat baths of different temperatures alternately, to mimic the macroscopic engine cycles like Carnot or Stirling. Due to the minute size of the system the fluctuations dominate. Recently it has been observed that presence of so called Active entities like Bacteria or Janus particles in the heat bath may drastically alter the thermodynamic properties, especially the efficiency of the engine, when compared with their passive counterparts. These are termed as Active Brownian Heat engines. I will discuss a few simple models of active heat engines that we have developed recently. I will also discuss a few general results that allow us to map such active, non-equilibrium system to an effective equilibrium system in the quasi-static limit of the cycle time.

Ref:-

1) https://iopscience.iop.org/article/10.1088/1742-5468/aae84a/meta

2) https://iopscience.iop.org/article/10.1088/1742-5468/ab39d4

3) https://arxiv.org/abs/2112.09561

4) https://journals.aps.org/pre/abstract/10.1103/PhysRevE.102.060101

The probability distribution of the total entropy production in the non- equilibrium steady state follows a symmetry relation called the fluctuation theorem. When a certain part of the system is masked or hidden, it is difficult to infer the exact estimate of the total entropy production. Entropy produced from the observed part of the system shows significant deviation from the steady-state fluctuation theorem. This deviation occurs due to the interaction between the observed and the masked part of the system. A naive guess would be that the deviation from the steady state fluctuation theorem may disappear in the limit of small interaction between both parts of the system.

Fermi pointed out that the Hydrogen atom in a thermal setting is unstable, as the canonical partition function of this simple system diverges. We show how a non-normalised Boltzmann Gibbs measure can still yield statistical averages and thermodynamic properties of physical observables, exploiting a model of Langevin dynamics of a Brownian particle in an asymptotically flat potential [1]. The ergodic theory of such systems is known in mathematics as infinite (non-normalisable) ergodic theory, time permitting we will discuss these isssues in the context of a gas of laser cooled atoms [2].

**References:**

[1] E. Aghion, D. A. Kessler, and E. Barkai From Non-normalizable Boltzmann-Gibbs statistics to infinite-ergodic theory Phys. Rev. Lett. 122, 010601 (2019).

[2] E. Barkai, G. Radons, and T. Akimoto Transitions in the ergodicity of subrecoil-laser-cooled gases Phys. Rev. Lett. 127, 140605 (2021).

Thursday, 16 June 2022

Replisomes are multi-protein complexes that replicate genomes with remarkable speed and accuracy. Despite their importance, their dynamics is poorly characterized, especially in vivo. We introduce a theory to infer the stochastic dynamics of replisomes from the DNA abundance observed in a growing bacterial population. We show, in particular, how this dynamics can be mapped into a two-dimensional stochastic process subject to stochastic resetting. To apply our theory, we present experiments with E.coli bacteria growing at different temperatures. Our theory reveals that replisome speed presents regular oscillations along the genome and is characterized by a small diffusion constant. We conclude with a discussion of the possible causes and consequences of this finding, and possible extensions of our theory.

Reference: https://www.biorxiv.org/content/10.1101/2021.10.15.464478v1

The entropy production, defined either microscopically or informatically at coarse-grained scale, is a key measure of irreversibility in active systems. This talk will address the large deviations of the entropy production: in a given system what is the probability of this being much larger or smaller than usual for a prolonged period, and what is the likeliest way for this to happen? Studying the full probability distribution for entropy production in this way reveals various nonequilibrium phase transitions, including some into symmetry-broken phases that are absent for dynamically typical states. These transitions point to design principles for active matter. Such studies are typically numerical, but for one well-chosen model (an active lattice gas) the nonequilibrium phase diagram can be calculated in its entirety, revealing unforeseen complexity.

TBA

While the fluctuation theorem in classical systems has been thoroughly generalized under various feedback control setups, the role of continuous measurement and feedback in the quantum regime has not yet been elucidated, despite its significance in quantum control. In this work, we derive the generalized fluctuation theorem with continuous measurement and feedback, by newly introducing the operationally meaningful quantum information, which we call quantum-classical-transfer (QC-transfer) entropy. QC-transfer entropy can be naturally interpreted as the quantum counterpart of transfer entropy that is commonly used in classical time series analysis. We also verify our theoretical results by numerical simulation and propose an experiment-numerics hybrid verification method. Our work reveals a fundamental connection between quantum thermodynamics and quantum information, which can be experimentally tested with artificial quantum systems such as circuit quantum electrodynamics.

Reference: T. Yada, N. Yoshioka, T. Sagawa, Phys. Rev. Lett. 128, 170601 (2022)

Long-time results for current fluctuations are often obtained within the framework of large deviation theory. Finite-time results are harder to get however due to the prevalence of transient effects and correlations. In this talk, I will mention some of the known results for finite and short- time current fluctuations, including some of our own.

I will then talk about two of our recent results. First, for biochemical oscillations, such as circadian rhythms, in stochastic systems, we have conjectured the universal minimal free energy cost of coherent oscillations. Second, active cyclic heat engines are heat engines with a working substance is in the presence of hidden dissipative degrees of freedom such as bacteria. In this case, the external bath is an active medium (or active matter). We have derived a generic second law for active heat engines, which has been a challenge since active heat engines have been introduced in an experiment in 2016.

**Study materials:**