Infinite family of second-law-like inequalities

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. Fil: Perez Espigares, Carlos. Universidad de Granada. Facultad de Ciencias. Departamento de Electromagnetismo y Física de la Materia. Instituto "Carlos I" de Física Teórica y Computacional; España Fil: Kolton, Alejandro Benedykt. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina