Inferring kinetics and entropy production from observable transitions in partially accessible, periodically driven Markov networks

TL;DR

This paper introduces a method for inferring transition rates, hidden states, and entropy production in periodically driven Markov networks from limited observational data.

Contribution

It develops an inference scheme for partially observable, periodically driven Markov networks, including bounds on entropy production and methods to estimate hidden transitions.

Findings

Inference of transition rates and hidden states from limited data

Lower bounds on entropy production in periodic states

Original results extending steady-state methods

Abstract

For a network of discrete states with a periodically driven Markovian dynamics, we develop an inference scheme for an external observer who has access to some transitions. Based on waiting-time distributions between these transitions, the periodic probabilities of states connected by these observed transitions and their time-dependent transition rates can be inferred. Moreover, the smallest number of hidden transitions between accessible ones and some of their transition rates can be extracted. We prove and conjecture lower bounds on the total entropy production for such periodic stationary states. Even though our techniques are based on generalizations of known methods for steady states, we obtain original results for those as well.