Thermo--hydrodynamics As a Field Theory

TL;DR

This paper develops a field theoretical framework for thermo-hydrodynamics, introducing a duality between physical and material space-time, and explores its canonical structure, conservation laws, and the role of material time as a temperature potential.

Contribution

It presents a novel field theory formulation of thermo-hydrodynamics based on dual space-time structures and introduces a material time as a temperature field potential.

Findings

Canonical formulation of thermo-hydrodynamics established

Poisson brackets and conservation laws derived

Material time identified as a temperature potential

Abstract

The field theoretical description of thermo-hydrodynamics is given. It is based on the duality between the physical space--time and the "material space-time" which we construct here. The material space appearing in a natural way in the canonical formulation of the hydrodynamics is completed with a material time playing role of the field potential for temperature. Both Lagrangian and Hamiltonian formulations, the canonical structure, Poisson bracket, N\"other theorem and conservation laws are discussed.