Compensating random transition-detection blackouts in Markov networks

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 not require the blackouts to occur homogeneously or symmetrically under time-reversal.