Informatic versus Thermodynamic Entropy Production in Active Systems
Stochastic thermodynamics connects the steady-state entropy production rate (EPR) of a system connected to a heat bath with the log ratio of probabilities of forward and time-reversed trajectories. Extending the resulting formula to coarse-grained models of systems much further from equilibrium, such as schools of fish or herds of wildebeest, results in an informatic EPR (IEPR) that depends only on order parameter dynamics and no longer is connected with microscopic heat flow, but remains a valuable quantifier of macroscopic irreversibility. I will discuss where the connection with heat flow gets lost, and the ambiguities caused by its absence. I will also consider cases where the same coarse-grained models describe more microscopic processes (such as motors moving along filaments in the cytoskeleton) for which a connection to heat flow should be recoverable. To achieve this we can embed thecoarse-grained model into a larger model involving explicit (if schematic) chemical reactions such that the whole system is governed by linear irreversible thermodynamics -- which applies whenever fluxes are linear in thermodynamic forces. (It does not require those forces to be linear in order parameters, so the full nonlinearity of the coarse grained active model is retained.) All the active terms in the order parameter dynamics then become off-diagonal elements of an Onsager matrix whose symmetry determines the remaining chemical couplings and thus the overall heat production. This exceeds the IEPR by a term that is a large constant in uniform systems, but contains additional spatial information in nonuniform ones.
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