Testing the irreversibility of a Gibbsian process via hitting and return times

Abstract

We introduce estimators for the entropy production of a Gibbsian process based on the observation of a single or two typical trajectories. These estimators are built with adequate hitting and return times. We then study their convergence and fluctuation properties. This provides statisticals test for the irreversibility of Gibbsian processes.

arXiv comment16 pages; Corrected version; To appear in Nonlinearity

References in corpus (4)

• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Dynamical ensembles in stationary states
• The Fluctuation Theorem as a Gibbs Property
• Large Deviations and a Fluctuation Symmetry for Chaotic Homeomorphisms

Cited by in corpus (4)

• Estimating entropy rate from censored symbolic time series: a test for time-irreversibility
• Recurrence times, waiting times and universal entropy production estimators
• On the entropy production of time series with unidirectional linearity
• Time-irreversibility tests for random-length time series: the matching-time approach applied to DNA