Elementary thermo-mechanical systems and higher order constraints

Abstract

In this paper we study a class of physical systems that combine a finite number of mechanical and thermodynamic observables. We call them elementary thermo-mechanical systems (ETMS). We introduce these systems by means of simple examples, and we obtain their (time) evolution equations by using, essentially, the Newton’s laws and the First Law of Thermodynamics only. We show that such equations are similar to those defining certain constrained mechanical systems. From that, and addressing the main aim of the paper, we give a general definition of ETMS, in a variational formalism, as a particular subclass of the Lagrangian higher order constrained systems.