On geometry of phenomenological thermodynamics

TL;DR

This paper reformulates phenomenological thermodynamics using even-dimensional symplectic geometry, providing clearer conceptual insights and advantages over the traditional contact structure approach.

Contribution

It introduces a symplectic geometric formalism for thermodynamics, highlighting conceptual clarifications and a gauge interpretation not present in previous models.

Findings

Symplectic geometry effectively captures thermodynamic structure.

Clarifies the geometric role of internal energy and potentials.

Provides a gauge interpretation of thermodynamic theory.

Abstract

We present the formalism of phenomenological thermodynamics in terms of the even-dimensional symplectic geometry, and argue that it catches its geometric essence in a more profound and clearer way than the popular odd-dimensional contact structure description. Among the advantages are a number of conceptual clarifications: the geometric role of internal energy (not made as an independent variable), the lattice of potentials, and the gauge interpretation of the theory.