Infinite family of second-law-like inequalities

CARLOS PÉREZ-ESPIGARES; ALEJANDRO B. KOLTON; JORGE KURCHAN

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

American Physical Society

Año: 2012 vol. 85 p. 31135 - 31143

1063-651X

The probability distribution function for an out of equilibrium system may sometimes be approximated by a physically motivated “trial” distribution. A particularly interesting case is when a driven system (e.g., active matter) is approximated by a thermodynamic one. We show here that every set of trial distributions yields an inequality playing the role of a generalization of the second law. The better the approximation is, the more constraining the inequality becomes: this suggests a criterion for its accuracy, as well as an optimization procedure that may be implemented numerically and even experimentally. The fluctuation relation behind this inequality, a natural and practical extension of the Hatano-Sasa theorem, does not rely on the a priori knowledge of the stationary probability distribution.