Information loss and entropy production during dissipative processes in a macroscopic system kicked out of the equilibrium

TL;DR

This paper investigates how information loss and entropy production occur in a macroscopic system returning to equilibrium after a kick, using stochastic thermodynamics to relate fluctuations, inverse problems, and thermodynamic limits.

Contribution

It introduces an information-theoretical framework linking fluctuations, entropy production, and inverse problems in dissipative processes, with applications to imaging resolution.

Findings

Derived the probability distribution and information loss for a kicked Brownian particle.

Showed the equality of information loss and entropy production in general dissipative processes.

Provided thermodynamic limits for spatial resolution in imaging based on fluctuations.

Abstract

In macroscopic systems behavior is usually reproducible and fluctuations, which are deviations from the typically observed mean values, are small. But almost all inverse problems in the physical and biological sciences are ill-posed and these fluctuations are highly 'amplified'. Using stochastic thermodynamics we describe a system in equilibrium kicked to a state far from equilibrium and the following dissipative process back to equilibrium. From the observed value at a certain time after the kick the magnitude of the kick should be estimated, which is such an ill-posed inverse problem and fluctuations get relevant. For the model system of a kicked Brownian particle the time-dependent probability distribution, the information loss about the magnitude of the kick described by the Kullback-Leibler divergence, and the entropy production derived from the observed mean values are given. The equality of information loss caused by fluctuations and mean entropy production is shown for general kicked dissipative processes from stochastic thermodynamics following the derivation of the Jarzynski and Crooks equalities. The information-theoretical interpretation of the Kullback-Leibler divergence (Chernoff-Stein Lemma) allows us to describe the influence of the fluctuations without knowing their distributions just from the mean value equations and thus to derive very applicable results, e.g., by giving thermodynamic limits of spatial resolution for imaging.