Strong Coupling Thermodynamics and Stochastic Thermodynamics from the Unifying Perspective of Time-Scale Separation

Abstract

Assuming time-scale separation, a simple and unified theory of thermodynamics and stochastic thermodynamics is constructed for small classical systems strongly interacting with its environment in a controllable fashion. The total Hamiltonian is decomposed into a bath part and a system part, the latter being the Hamiltonian of mean force. Both the conditional equilibrium of bath and the reduced equilibrium of the system are described by canonical ensemble theories with respect to their own Hamiltonians. The bath free energy is independent of the system variables and the control parameter. Furthermore, the weak coupling theory of stochastic thermodynamics becomes applicable almost verbatim, even if the interaction and correlation between the system and its environment are strong and varied externally. Finally, this TSS-based approach also leads to some new insights about the origin of the second law of thermodynamics.

12 pages

References in corpus (6)

• Fluctuation Theorem for Arbitrary Open Quantum Systems
• Thermodynamics of a subensemble of a canonical ensemble
• Covariant Formulation of Non-linear Langevin Theory with Multiplicative Gaussian White Noises
• Strong Coupling Quantum Thermodynamics with Renormalized Hamiltonian and Temperature
• Zeroth Law in Quantum Thermodynamics at Strong Coupling: `in Equilibrium', not `Equal Temperature'
• Covariant Non-equilibrium Thermodynamics from Ito-Langevin Dynamics

Cited by in corpus (2)

• Quantum Otto engine with quantum correlations
• Stochastic energetics of a colloidal particle trapped in a viscoelastic bath