Milestoning estimators of dissipation in systems observed at a coarse resolution: When ignorance is truly bliss

TL;DR

This paper demonstrates that ignoring parts of coarse-grained state space via milestoning can improve estimates of entropy production in non-equilibrium systems, even when the physical definition of time-reversal with memory is uncertain.

Contribution

It introduces milestoning as a method to enhance thermodynamic inference from coarse observations by effectively accounting for memory effects in semi-Markov processes.

Findings

Milestoning improves entropy-production estimates from lumped data.

Ignoring parts of the state space can make observations closer to microscopic dynamics.

Naive Markovian time-reversal definitions often require discarding waiting-time contributions.

Abstract

Many non-equilibrium, active processes are observed at a coarse-grained level, where different microscopic configurations are projected onto the same observable state. Such "lumped" observables display memory, and in many cases the irreversible character of the underlying microscopic dynamics becomes blurred, e.g., when the projection hides dissipative cycles. As a result, the observations appear less irreversible, and it is very challenging to infer the degree of broken time-reversal symmetry. Here we show, contrary to intuition, that by ignoring parts of the already coarse-grained state space we may -- via a process called milestoning -- improve entropy-production estimates. Milestoning systematically renders observations "closer to underlying microscopic dynamics" and thereby improves thermodynamic inference from lumped data assuming a given range of memory. Moreover, whereas the correct general physical definition of time-reversal in the presence of memory remains unknown, we here show by means of systematic, physically relevant examples that at least for semi-Markov processes of first and second order, waiting-time contributions arising from adopting a naive Markovian definition of time-reversal generally must be discarded.