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.
Highlights
Systems coupled to multiple thermodynamic reservoirs can exhibit nonequilibrium dynamics, breaking detailed balance to generate currents
A direct local calorimetric measurement is challenging, but signatures of the dissipation are encoded in stochastic fluctuations of the system[20], even far-fromequilibrium[21,22,23,24,25,26,27,28,29]
The bead-spring model allows us to address various practical considerations that will be important for future experimental applications of the inference techniques: how much data is required, what is the role of coarse graining, and what can be done about the curse of dimensionality
Summary
Systems coupled to multiple thermodynamic reservoirs can exhibit nonequilibrium dynamics, breaking detailed balance to generate currents. 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. The energetic loss can alternatively be cast as an increase in entropy of the environment, and the entropy production is associated with broken time-reversal symmetry in the system’s dynamics[5,6,7] This connection has been leveraged to experimentally classify particular biophysical processes as thermal or active[8,9] based on the existence of probability currents[10,11]. There is great interest in going beyond this binary classification— thermal versus active—to experimentally quantify how active, or how nonequilibrium, a process is[12,13,14] Such a quantification could, for example, provide insight into how efficiently molecular motors are able to work together to drive large-scale motions[15,16,17,18,19]. We anticipate many of these insights will support the data analysis of experimentally accessible biological and active matter systems
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