A Hamilton-Jacobi Formalism for Thermodynamics

Understand

We show that classical thermodynamics has a formulation in terms of Hamilton-Jacobi theory, analogous to mechanics.

• Even though the thermodynamic variables come in conjugate pairs such as pressure/volume or temperature/entropy, the phase space is odd-dimensional.
• For a system with n thermodynamic degrees of freedom it is (2n+1)-dimensional.
• The equations of state of a substance pick out an n-dimensional submanifold.