Infinite family of second-law-like inequalities

Details Infinite family of second-law-like inequalities Infinite family of second-law-like inequalities

2011-10-05

arxiv.org/abs/1110.0967v3

Phys. Rev. E 85, 031135 (2012)

Physics

Condensed Matter

Statistical Mechanics

9 pages, 3 figures

Scientific paper

10.1103/PhysRevE.85.031135

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.

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