English

Thermodynamic reduction of contact dynamics

Dynamical Systems 2025-04-24 v2 Symplectic Geometry

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.

Keywords

Cite

@article{arxiv.2412.19319,
  title  = {Thermodynamic reduction of contact dynamics},
  author = {Hyun-Seok Do and Yong-Geun Oh},
  journal= {arXiv preprint arXiv:2412.19319},
  year   = {2025}
}

Comments

35 pages, v2) 41 pages, one more appendix added, references updated, subsection 9.2 rewritten