Hamilton-Jacobi approach to thermodynamic transformations

Abstract

In this note, we formulate and study a Hamilton-Jacobi approach for describing thermodynamic transformations. The thermodynamic phase space assumes the structure of a contact manifold with the points representing equilibrium states being restricted to certain submanifolds of this phase space. We demonstrate that Hamilton-Jacobi theory consistently describes thermodynamic transformations on the space of externally controllable parameters or equivalently, the space of equilibrium states. It turns out that in the Hamilton-Jacobi description, the choice of the principal function is not unique but, the resultant dynamical description for a given transformation remains the same irrespective of this choice. Some examples involving thermodynamic transformations of the ideal gas are discussed where the characteristic curves on the space of equilibrium states completely describe the dynamics. The geometric Hamilton-Jacobi formulation which has emerged recently is also discussed in the context of thermodynamics.

arXiv commentv1: Preliminary version; v2: Revised version; v3: Typos corrected

References in corpus (16)

• Measuring thermodynamic length
• Thermodynamic metrics and optimal paths
• Repulsive Interactions and Universal Properties of Charged Anti-de Sitter Black Hole Microstructures
• Thermodynamic Geometry and Critical Behavior of Black Holes
• Contact Hamiltonian Mechanics
• Geometrothermodynamics of black holes
• Ruppeiner Geometry, Phase Transitions, and the Microstructure of Charged AdS Black Holes
• The geometry of thermodynamic control
• Cosymplectic and contact structures to resolve time-dependent and dissipative hamiltonian systems
• Contact Symmetries and Hamiltonian Thermodynamics
• A Hamilton-Jacobi Formalism for Thermodynamics
• Contact geometry and thermodynamics of black holes in AdS spacetimes
• Multiscale Thermodynamics
• Reviewing the Geometric Hamilton-Jacobi Theory concerning Jacobi and Leibniz identities
• A Hamiltonian approach for the Thermodynamics of AdS black holes
• An eikonal equation approach to thermodynamics and the gradient flows in information geometry

Cited by in corpus (1)

• Invariant measures for some dissipative systems from the Jacobi last multiplier