Finite dimensional thermo-mechanical systems and second order constraints

TL;DR

This paper introduces finite dimensional thermo-mechanical systems, demonstrating their equations of motion derived from fundamental physical laws and their description via second order constrained variational formalism.

Contribution

It defines a new class of physical systems combining mechanical and thermodynamic variables and shows their equations can be formulated as second order constrained systems.

Findings

Equations derived from Newton's law and thermodynamics.

Examples modeled as higher order constrained systems.

Variational formalism applicable to all examples.

Abstract

In this paper we study a class of physical systems that combine a finite number of mechanical and thermodynamic observables. We call them finite dimensional thermo-mechanical systems. We introduce these systems by means of simple examples. The evolution equations of the involved observables are obtained in each example by using, essentially, the Newton's law and the First Law of Thermodynamics only. We show that such equations are similar to those defining certain mechanical systems with higher order constraints. Moreover, we show that all of the given examples can be described in a variational formalism in terms of second order constrained systems.