A nonequilibrium distribution for stochastic thermodynamics

The canonical distribution of Gibbs is extended to the case of systems outside equilibrium. The distribution of probabilities of a discrete energy levels system is used to provide a microscopic definition of work, along with a microscopic definition of the uncompensated heat of Clausius involved in nonequilibrium processes. The later is related to the presence of non-conservatives forces with regards to the variation of the external parameters. This new framework is used to investigate the nonequilibrium relations in stochastic thermodynamics. A new relation is derived for the random quantity of heat associated to the nonequilibrium work protocol. We finally show that the distributions of probabilities of work, heat and uncompensated heat are non-independent each other during a nonequilibrium process.