Microscopic basis of stochastic thermodynamics

There is a revolution underway in nonequilibrium statistical physics. The emerging framework of stochastic thermodynamics has enabled us to define the thermodynamic concepts of work, energy, heat, entropy, and entropy production at the level of individual trajectories of stochastic systems, even if the system is far from equilibrium. Here we provide a microscopic, Hamiltonian basis underlying stochastic thermodynamics by using an explicit representation of the heat bath. The irreversibility of the system at the stochastic level arises from an improbable initial condition and the infinite nature of the heat bath at the Hamiltonian level. We have explicitly identified the different expressions of heat and entropy production in these two levels of description. This work provides a new unifying connection between different levels of description of nonequilibrium statistical physics.