Estimating entropy production from waiting time distributions

TL;DR

This paper introduces a new method to estimate entropy production in biological systems using waiting time distributions, enabling analysis of non-equilibrium behavior from experimental data despite hidden variables.

Contribution

The authors develop a universal bounding technique for entropy production based solely on waiting time statistics of hidden Markov processes, applicable to diverse biological data.

Findings

Boundaries on entropy production derived from experimental data.

Application to gene networks and behavioral dynamics.

Estimated entropic costs of heartbeat regulation in humans, dogs, and mice.

Abstract

Living systems operate far from thermal equilibrium by converting the chemical potential of ATP into mechanical work to achieve growth, replication or locomotion. Given time series observations of intra-, inter- or multicellular processes, a key challenge is to detect non-equilibrium behavior and quantify the rate of free energy consumption. Obtaining reliable bounds on energy consumption and entropy production directly from experimental data remains difficult in practice as many degrees of freedom typically are hidden to the observer, so that the accessible coarse-grained dynamics may not obviously violate detailed balance. Here, we introduce a novel method for bounding the entropy production of physical and living systems which uses only the waiting time statistics of hidden Markov processes and hence can be directly applied to experimental data. By determining a universal limiting curve, we infer entropy production bounds from experimental data for gene regulatory networks, mammalian behavioral dynamics and numerous other biological processes. Further considering the asymptotic limit of increasingly precise biological timers, we estimate the necessary entropic cost of heartbeat regulation in humans, dogs and mice.