Quantitative analysis of non-equilibrium systems from short-time experimental data

Abstract

Estimating entropy production directly from experimental trajectories is of great current interest but often requires a large amount of data or knowledge of the underlying dynamics. In this paper, we propose a minimal strategy using the short-time Thermodynamic Uncertainty Relation (TUR) by means of which we can simultaneously and quantitatively infer the thermodynamic force field acting on the system and the (potentially exact) rate of entropy production from experimental short-time trajectory data. We benchmark this scheme first for an experimental study of a colloidal particle system where exact analytical results are known, prior to studying the case of a colloidal particle in a hydrodynamical flow field, where neither analytical nor numerical results are available. In the latter case, we build an effective model of the system based on our results. In both cases, we also demonstrate that our results match with those obtained from another recently introduced scheme.

Passive probe particle in an active bath: can we tell it is out of equilibrium?

“…Among other non-equilibrium signatures proposed in the literature, [47][48][49][50][51] one of the most ubiquitous is entropy production associated with a difference of probabilities between forward and time-reversed trajectories, which has been found in a number of active systems including that of an isolated active Langevin particle 24 and that of many interacting active Brownian particles undergoing MIPS. 52 In particular, ref.…”

Inferring entropy production in anharmonic Brownian gyrators

“…We see that they fall on top of each other, and agree with the functional behaviour given in Eq. (15). In Fig.…”

“…[12,13], and recently tested in a colloidal experimental setup in Ref. [15]. Using this technique, we can obtain the steady-state entropy production rate as, where J is a weighted scalar current defined as…”

“…In recent work, the feasibility of this inference scheme was tested on experiments with a colloidal particle in a time-varying potential [15], where it was shown that the method correctly reproduces the entropy production rate and the thermodynamic force field known by other theoretical means.…”

Time to reach the maximum for a stationary stochastic process

“…Throughout the last decades, several methods to determine the nonequilibrium nature of a system have been developed -for a recent review, see [50]. Many of these techniques also quantify how much the system is out of equilibrium, usually as a bound on the entropy production [88][89][90][91][92]. A popular technique is based on the verification of the fluctuation-dissipation relation, which relates correlation and response for equilibrium systems [93][94][95][96].…”