Skewness and Kurtosis in Stochastic Thermodynamics

TL;DR

This paper investigates higher order moments like skewness and kurtosis in stochastic thermodynamics, developing methods to evaluate them and proposing bounds for unicyclic systems, with implications for understanding underlying network structures.

Contribution

It introduces a method to evaluate skewness and kurtosis of first passage times in stochastic thermodynamics and proposes bounds for unicyclic networks, extending the understanding of fluctuations beyond variance.

Findings

Bounds on skewness and kurtosis depend on system states and driving force.

Bounds do not hold for multicyclic networks.

Method enables inference of underlying network structure.

Abstract

The thermodynamic uncertainty relation is a prominent result in stochastic thermodynamics that provides a bound on the fluctuations of any thermodynamic flux, also known as current, in terms of the average rate of entropy production. Such fluctuations are quantified by the second moment of the probability distribution of the current. The role of higher order standardized moments such as skewness and kurtosis remains largely unexplored. We analyze the skewness and kurtosis associated with the first passage time of thermodynamic currents within the framework of stochastic thermodynamics. We develop a method to evaluate higher order standardized moments associated with the first passage time of any current. For systems with a unicyclic network of states, we conjecture upper and lower bounds on skewness and kurtosis associated with entropy production. These bounds depend on the number of states and the thermodynamic force that drives the system out of equilibrium. We show that these bounds for skewness and kurtosis do not hold for multicyclic networks. We discuss the application of our results to infer an underlying network of states.