ICTS

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.

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.      

[1] https://scipost.org/10.21468/SciPostPhys.12.4.139

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.

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).

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

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)

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:

1) arXiv:2112.01607

2) arXiv:2112.03986