• Corpus ID: 252439110

Nonequilibrium thermodynamics as a symplecto-contact reduction and relative information entropy

@inproceedings{Lim2022NonequilibriumTA,
  title={Nonequilibrium thermodynamics as a symplecto-contact reduction and relative information entropy},
  author={Jin-wook Lim and Yong Geun Oh},
  year={2022}
}

• Jin-wook Lim, Y. Oh
• Published 21 September 2022
• Physics

. Both statistical phase space (SPS), Γ = T ∗ R 3 N of N -body particle system F , and kinetic theory phase space (KTPS), 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. Regarding the collective observation of observables 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 an (in- finite dimensional) symplectic fibration. We then show that the F -reduction of the relative information entropy (aka Kullback-Leibler divergence) defines a generating function that provides a covariant construction of thermodynamic equilibrium as a Legendrian submanifold. This Legendrian submanifold is not necessarily holonomic. We interpret the Maxwell construction as the procedure of finding a continuous, not necessarily differentiable, thermodynamic potential and explain the associated phase transition. We do this by identify-ing the procedure with that of finding a graph selector in symplecto-contact geometry and in the Aubry-Mather theory of dynamical system. Our derivation complements the previously proposed contact geometric description of thermodynamic equilibria and explains the origin of phase transition and the Maxwell construction in this framework.