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Abstract: The Caldeira–Leggett Hamiltonian describes the interaction of a discrete harmonic oscillator with a continuous bath of harmonic oscillators. This system is a standard model of dissipation in macroscopic low temperature physics, and has applications to superconductors, quantum computing, and macroscopic quantum tunneling. The similarities between the Caldeira–Leggett model and the linearized Vlasov–Poisson equation are analyzed, and it is shown that the damping in the Caldeira–Leggett model is analogous to that of Landau damping in plasmas (Landau, 1946 ). An invertible linear transformation (Morrison and Pfirsch, 1992 ; Morrison, 2000 ) is presented that converts solutions of the Caldeira–Leggett model into solutions of the linearized Vlasov–Poisson system. [Copyright &y& Elsevier]

The change of the von Neumann entropy of a set of harmonic oscillators initially in thermal equilibrium and interacting linearly with an externally driven quantum system is computed by adapting the Feynman–Vernon influence functional formalism. This quantum entropy production has the form of the expectation value of three functionals of the forward and backward paths describing the system history in the Feynman–Vernon theory. In the classical limit of Kramers–Langevin dynamics (Caldeira–Leggett model) these functionals combine to three terms, where the first is the entropy production functional of stochastic thermodynamics, the classical work done by the system on the environment in units of k _B T, and the second and the third other functionals which have no analogue in stochastic thermodynamics.