Geometrical Thermodynamic Field Theory

TL;DR

This paper reformulates Thermodynamic Field Theory in a covariant, coordinate-independent way, introducing the Minimum Dissipation Principle and deriving simplified field equations applicable beyond weak-field regimes.

Contribution

It presents a manifestly covariant reformulation of TFT, introduces the Minimum Dissipation Principle, and derives new, simpler thermodynamic field equations for general cases.

Findings

Derived thermodynamic field equations for complex processes.

Proposed the Minimum Dissipation Principle for systems relaxing to steady-state.

Identified conditions for steady-states and their stability.

Abstract

A manifestly covariant, coordinate independent reformulation of the Thermodynamic Field Theory (TFT) is presented. The TFT is a covariant field theory that describes the evolution of a thermodynamic system, extending the near-equilibrium theory established by Prigogine in 1954. We introduce the {\it Minimum Dissipation Principle}, which is conjectured to apply to any system relaxing towards a steady-state. We also derive the thermodynamic field equations, which in the case of alpha-alpha and beta-beta processes have already appeared in the literature. In more general cases the equations are notably simpler than those previously encountered and they are conjectured to hold beyond the weak-field regime. Finally we derive the equations that determine the steady-states as well as the critical values of the control parameters beyond which a steady-state becomes unstable.