  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.
