Compensating random transition-detection blackouts in Markov networks

TL;DR

This paper introduces a method to correct for measurement blackouts in Markov networks, enabling accurate inference of thermodynamic quantities and entropy production despite data loss.

Contribution

The authors propose a novel approach that attributes blackouts to a second transition channel, allowing recovery of true transition rates and entropy bounds from incomplete data.

Findings

Effective correction of blackout effects in Markov networks.

Recovery of entropy production bounds from post-processed data.

Applicability without assumptions on blackout symmetry or homogeneity.

Abstract

In Markov networks, measurement blackouts with unknown frequency compromise observations such that thermodynamic quantities can no longer be inferred reliably. In particular, the observed currents neither discern equilibrium from non-equilibrium nor can they be used in extant estimators of entropy production. Our strategy to eliminate these effects is based on formally attributing the blackouts to a second channel connecting states. The unknown frequency of blackouts and the true underlying transition rates can be determined from the short-time limit of observed waiting-time distributions. A post-modification of observed trajectory data yields a virtual effective dynamics from which the lower bound on entropy production based on thermodynamic uncertainty relations can be recovered fully. Moreover, the post-processed data can be used in waiting-time based estimators. Crucially, our strategy does neither require the blackouts to occur homogeneously nor symmetrically under time-reversal.