Fluctuation theorems and inequalities generalizing the second law of thermodynamics out of equilibrium

摘要

We present a general framework for systems which are prepared in a nonstationary nonequilibrium state innthe absence of any perturbation and which are then further driven through the application of a time-dependentnperturbation. By assumption, the evolution of the system must be described by Markovian dynamics. Wendistinguish two different situations depending on the way the nonequilibrium state is prepared; either it is creatednby some driving or it results from a relaxation following some initial nonstationary conditions. Our approachnis based on a recent generalization of the Hatano-Sasa relation for nonstationary probability distributions. Wenalso investigate whether a form of the second law holds for separate parts of the entropy production and fornany nonstationary reference process, a question motivated by the work of M. Esposito et al. [Phys. Rev. Lett.n104, 090601 (2010)]. We find that although the special structure of the theorems derived in this reference is notnrecovered in the general case, detailed fluctuation theorems still hold separately for parts of the entropy production.nThese detailed fluctuation theorems contain interesting generalizations of the second law of thermodynamics fornnonequilibrium systems.