Stroboscopic measurements in Markov networks: Exact generator reconstruction vs. thermodynamic inference

TL;DR

This paper compares two methods for estimating thermodynamic quantities in stroboscopically observed Markov networks, showing that generator reconstruction can outperform lower-bound approaches under certain measurement timescales.

Contribution

It introduces a comparison between generator reconstruction and entropy production bounds in stroboscopic Markov dynamics, highlighting the conditions under which each method is effective.

Findings

Generator reconstruction recovers all thermodynamic quantities when measurement times are sufficiently small.

Reconstruction provides tighter bounds than traditional lower-bound methods beyond a critical measurement interval.

Numerical illustrations demonstrate the advantages and limitations of both approaches.

Abstract

A major goal of stochastic thermodynamics is to estimate the inevitable dissipation that accompanies particular observable phenomena in an otherwise not fully accessible system. Quantitative results are often formulated as lower bounds on the total entropy production, which capture the part of the total dissipation that can be determined based on the available data alone. In this work, we discuss the case of a continuous-time dynamics on a Markov network that is observed stroboscopically, i.e., at discrete points in time in regular intervals. We compare the standard approach of deriving a lower bound on the entropy production rate in the steady state to the less common method of reconstructing the generator from the observed propagators by taking the matrix logarithm. Provided that the timescale of the stroboscopic measurements is smaller than a critical value that can be determined from the available data, this latter method is able to recover all thermodynamic quantities like entropy production or cycle affinities and is therefore superior to the usual approach of deriving lower bounds. Beyond the critical value, we still obtain tight upper and lower bounds on these quantities that improve on extant methods. We conclude the comparison with numerical illustrations and a discussion of the requirements and limitations of both methods.