Hamiltonian variational formulation for nonequilibrium thermodynamics of simple closed systems

TL;DR

This paper extends Hamilton's variational principles to nonequilibrium thermodynamics of simple closed systems, incorporating constraints and degeneracies, providing a new theoretical framework.

Contribution

It introduces a Hamiltonian variational formulation for thermodynamics using a Hamilton-d'Alembert principle and Dirac's constraints, extending mechanics principles to thermodynamic systems.

Findings

Formulated a Hamiltonian approach for thermodynamics.

Applied the framework to systems with friction and chemical reactions.

Demonstrated the method with illustrative examples.

Abstract

In this paper, we develop a Hamiltonian variational formulation for the nonequilibrium thermodynamics of simple adiabatically closed systems that is an extension of Hamilton's phase space principle in mechanics. We introduce the Hamilton-d'Alembert principle for thermodynamic systems by considering nonlinear nonholonomic constraints of thermodynamic type. In particular, for the case in which the given Lagrangian is degenerate, we construct the Hamiltonian by incorporating the primary constraints via Dirac's theory of constraints. We illustrate our Hamiltonian variational formulation with some examples of systems with friction, with internal matter transfer as well as with chemical reactions.