Nonequilibrium thermodynamics as a symplecto-contact reduction and relative information entropy
SCIE
SCOPUS
- Title
- Nonequilibrium thermodynamics as a symplecto-contact reduction and relative information entropy
- Authors
- OH, YONG GEUN; Lim, Jin-wook
- Date Issued
- 2023-12
- Publisher
- Pergamon Press Ltd.
- Abstract
- Both statistical phase space (SPS), which is Γ = T*R3N of N-body particle system, and kinetic theory phase space (KTPS), which is the cotangent bundle T*P(Γ) of the probability space P(Γ) thereon, carry canonical symplectic structures. Starting from this first principle, we provide a canonical derivation of thermodynamic phase space (TPS) of nonequilibrium thermodynamics as a contact manifold in two steps. First, regarding the collective observation of observables in SPS as a moment map defined on KTPS, we apply the Marsden–Weinstein reduction and obtain a mesoscopic phase space in between KTPS and TPS as a (infinite-dimensional) symplectic fibration. Then we show that the reduced relative information entropy defines a generating function that provides a covariant construction of a thermodynamic equilibrium as a Legen-drian submanifold. This Legendrian submanifold is not necessarily graph-like. We interpret the Maxwell construction of equal-area law as the procedure of finding a continuous, not necessarily differentiable, thermodynamic potential and explain the associated phase transition by identifying the procedure with that of finding a graph selector in symplecto-contact geometry and in the Aubry-Mather theory of dynamical system. © 2023 Polish Scientific Publishers PWN SA Warszawa
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/120915
- DOI
- 10.1016/S0034-4877(23)00084-8
- ISSN
- 0034-4877
- Article Type
- Article
- Citation
- Reports on Mathematical Physics, vol. 92, no. 3, page. 347 - 400, 2023-12
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