A Hamiltonian approach to Thermodynamics
Abstract
In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has welldefined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac's theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases.
 Publication:

Annals of Physics
 Pub Date:
 October 2016
 DOI:
 10.1016/j.aop.2016.07.004
 arXiv:
 arXiv:1604.03117
 Bibcode:
 2016AnPhy.373..245B
 Keywords:

 Thermodynamics;
 Hamiltonian formulation;
 Thermodynamic equation of state;
 Constrained systems;
 High Energy Physics  Theory;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics
 EPrint:
 11 pages, published version