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arXiv · 2412.19319

Thermodynamic reduction of contact dynamics

Hyun-Seok Do·Yong-Geun Oh
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Abstract

A universal algorithm to derive a macroscopic dynamics from the microscopic dynamical system via the averaging process and symplecto-contact reduction was introduced by Jin-wook Lim and the second-named author in [LO23]. They apply the algorithm to derive non-equilibrium thermodynamics from the statistical mechanics utilizing the relative information entropy as a generating function of the associated thermodynamic equilibrium. In the present paper, we apply this algorithm to the contact Hamiltonian dynamical systems. We describe a procedure of obtaining a discrete set of dynamical invariants of the given contact Hamiltonian system, or more generally of a contact multi-Hamiltonian system in a canonical way by deriving a (finite-dimensional non-equilibrium) thermodynamic system. We call this reduction the thermodynamic reduction of contact dynamics.

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Hyun-Seok Do, Yong-Geun Oh. 2024-12-26. Thermodynamic reduction of contact dynamics. https://arxiv.org/abs/2412.19319

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