Extreme value statistics of edge currents in Markov jump processes and their use for entropy production estimation

Understand

The infimum of an integrated current is its extreme value against the direction of its average flow.

• Using martingale theory, we show that the infima of integrated edge currents in time-homogeneous Markov jump processes are geometrically distributed, with a mean value determined by the effective affinity measured by a marginal observer that only sees the integrated edge current.
• In addition, we show that a marginal observer can estimate a finite fraction of the average entropy production rate in the underlying nonequilibrium process from the extreme value statistics in the integrated edge current.
• The estimated average rate of dissipation obtained in this way equals the above mentioned effective affinity times the average edge current.