Quantifying dissipation using fluctuating currents

Abstract

Systems coupled to multiple thermodynamic reservoirs can exhibit nonequilibrium dynamics, breaking detailed balance to generate currents. To power these currents, the entropy of the reservoirs increases. The rate of entropy production, or dissipation, is a measure of the statistical irreversibility of the nonequilibrium process. By measuring this irreversibility in several biological systems, recent experiments have detected that particular systems are not in equilibrium. Here we discuss three strategies to replace binary classification (equilibrium versus nonequilibrium) with a quantification of the entropy production rate. To illustrate, we generate time-series data for the evolution of an analytically tractable bead-spring model. Probability currents can be inferred and utilized to indirectly quantify the entropy production rate, but this approach requires prohibitive amounts of data in high-dimensional systems. This curse of dimensionality can be partially mitigated by using the thermodynamic uncertainty relation to bound the entropy production rate using statistical fluctuations in the probability currents.

Entropy production for coarse-grained dynamics

“…This would result in a deeper understanding of the microscopic world hidden behind a coarse-grained description. It would also have consequences in fields ranging from artificial molecular motors [9,26,30] to the possible quantification of the dissipation in biological systems [10] through the celebrated thermodynamic uncertainty relations [8]. Furthermore, our results can be applied to cases where an evolution occurs over a generic state space such as in interacting ecological and social systems (e.g.…”

“…Among all the possible quantities that can be estimated in a system out of equilibrium, in this work we focus on the entropy production, a fingerprint of non-equilibrium conditions. Recently, its crucial role in the outmost thermodynamic uncertainty relations [8,9] has been pointed out, along with the possibility to use the entropy production as a possible quantification of the non-equilibrium activity of a biological system [10]. It is also a fundamental quantity involved in various fluctuation theorems [11][12][13][14][15][16][17][18], whose theoretical relevance has stimulated several experimental confirmations in the field of stochastic thermodynamics [19][20][21].…”

Inferring Entropy Production from Short Experiments

“…Recently, for non-equilibrium systems in a steady state, such a scheme for identifying σ has been proposed [29,32] using the thermodynamic uncertainty relation [33,34]. Using this scheme, a lower bound σ L for σ can be obtained from the measurement of any fluctuating current J, in terms of its mean J and variance Var(J) as,…”

“…How tight this bound is depends in general on model details and the J chosen. As a result, there has been much interest recently on how to choose J such that the bound value is the tightest [32,38]. For τ → ∞, it is known that the current J that gives the best bound is J = ∆S tot [36].…”

Thermodynamic uncertainty relations including measurement and feedback

“…These include thermodynamic uncertainty relations (TURs) [10,11] as well as fluctuation relations [1,12,13], both of which have significantly contributed to our understanding of nonequilibrium phenomena (e.g., work extraction using measurement and feedback [14] and biological clocks [15]). A particularly interesting application of TURs is the inference of dissipation from the measurement of fluctuating currents [16]. While these relations have mostly been treated independently, a connection between TURs and fluctuation relations was recently established under rather restrictive assumptions [17][18][19].…”