An ergodic process of zero divergence-distance from its time-reversed process

2016/05/30 by David Andrieux, Andrieux, David · 1 citation
Computer Science · Neuroscience · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Cognitive Science and Education Research #FOS: Physical sciences #Neural Networks and Applications #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.1605.09355

openalex publication_date 2016/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An ergodic process P is constructed such that the divergence-rate D(P || P^*) is zero, yet P is not equal to its time-reversed process P^*. The process P is constructed as a special realization of the universal coding found by Xu. This result shows that there exist time-asymmetric processes that are indistinguishable under time-reversal and that can, in principle, be generated with zero dissipation.

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