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Microscopic Irreversibility And Gibbs Entropy, John D. Ramshaw

Physics Faculty Publications and Presentations

In a recent paper of the same title [J. Non-Equilib. Thermodyn., 15 (1990), 151], Liboff observed that the fine-grained Gibbs entropy of a canonical Hamiltonian system remains constant in time even for Hamiltonians that are not even in momenta and consequently violate time-reversal invariance (TRI). Here we extend this observation to non-canonical Hamiltonian systems, including systems with singular Poisson tensors and pseudo-Hamiltonian systems that violate the Jacobi identity. Necessary and sufficient conditions are given for the Gibbs entropy to be constant in such systems. The concept of TRI is not in general meaningful for such systems, but it is shown …