Stochastic Thermodynamics of Highly Underdamped Homogeneous Hamiltonian Systems

A systematic tutorial and semi-review develops a density-of-states-consistent stochastic thermodynamics for highly underdamped Hamiltonian systems from established Kramers energy diffusion. Positive homogeneous Hamiltonians organize exact energy, heat, entropy-production, work, protocol, cycle, and interacting graph-cage results by effective degrees of freedom and the relaxation rate.