The thermodynamic hamiltonian for open systems

TL;DR

This paper develops a general variational approach to derive the thermodynamic Hamiltonian for open systems, emphasizing irreversibility as the key driver of their evolution based on non-equilibrium thermodynamics.

Contribution

It introduces a novel method to obtain the thermodynamic Hamiltonian for open systems using a Lagrangian framework rooted in maximum entropy generation principles.

Findings

Irreversibility drives the evolution of open systems.

A variational method for thermodynamic Hamiltonian is established.

The approach links non-equilibrium thermodynamics with Hamiltonian mechanics.

Abstract

The variational method is very important in mathematical and theoretical physics because it allows us to describe the natural systems by physical quantities independently from the frame of reference used. A global and statistical approach have been introduced starting from non-equilibrium thermodynamics, obtaining the principle of maximum entropy generation for the open systems. This principle is a consequence of the lagrangian approach to the open systems. Here it will be developed a general approach to obtain the thermodynamic hamiltonian for the dynamical study of the open systems. It follows that the irreversibility seems to be the fundamental phenomenon which drives the evolution of the states of the open systems.