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Mathematical Physics Seminar

Informatic and Thermodynamic Entropy Production in Active Systems

Michael Cates - University of Cambridge

Location:  Zoom
Date & time: Wednesday, 26 January 2022 at 10:45AM - 11:45AM

Abstract: For a near-equilibrium system connected to a heat bath, there is a fundamental relationship between the steady-state entropy production rate (EPR) and the log of the ratio of probabilities of forward and time reversed trajectories. I will illustrate this first in the context of a single particle, and then explain how the result generalizes, in principle, to coarse-grained models of active matter, described by field theories. In practice, however, these theories often address systems extremely FAR from equilibrium, such as schools of fish or herds of wildebeest, for which the connection between macroscopic dynamics and microscopic heat flow is tenuous (at best).
In these cases we can nonetheless calculate an informatic counterpart of EPR that depends only on the coarse-grained dynamics and turns out to be a very useful quantifier of macroscopic irreversibility. In other situations, the same coarse-grained models are used to describe processes that are relatively microscopic and not so far from equilibrium, such as phase separation within a biological cell. Here a connection to heat flow should remain intact. I will show how to identify it by embedding the coarse-grained model into a larger model with explicit chemical reactions and heat flows, such that the whole system is governed by linear irreversible thermodynamics. 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 full heat production.