2024/10/06 by Ghosh, Aritra, Harikumar, E. · 1 citation
#Classical Physics (physics.class-ph) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2410.04622
We describe a symplectic approach to thermodynamics in which thermodynamic transformations are described by Hamiltonian dynamics on thermodynamic spaces. By identifying the spaces of equilibrium states with Lagrangian submanifolds of a symplectic manifold, we construct a Hamiltonian description of thermodynamic processes where the space of equilibrium states of a system in a certain ensemble is the level set on which the Hamiltonian takes a constant value. In particular, we work out two explicit examples involving the ideal gas. Finally, we describe a Hamiltonian approach towards constructing maps between related thermodynamic systems, e.g., the ideal (non-interacting) gas and interacting gases.