Thermo--hydrodynamics As a Field Theory

Understand

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.