Eur. Phys. J. B (2012) 85: 412
https://doi.org/10.1140/epjb/e2012-30719-4

Regular Article

Thermodynamics of continuous media with electromagnetic fields

Institute of Condensed Matter Physics, Station 3, École Polytechnique Fédérale de Lausanne – EPFL, 1015 Lausanne, Switzerland

^a e-mail: sylvain.brechet@epfl.ch
^b e-mail: francois.reuse@epfl.ch
^c e-mail: jean-philippe.ansermet@epfl.ch

Received: 3 August 2012
Received in final form: 24 October 2012
Published online: 20 December 2012

Abstract

The thermodynamics of an electrically charged, multicomponent continuous medium with electromagnetic fields is analysed in the non-relativistic limit. Applying locally the first and second law of thermodynamics and Maxwell’s equations for a linear theory of electromagnetism, three equations characterising the continuous medium are derived: a thermostatic equilibrium equation, a reversible and an irreversible thermodynamic evolution equation. For a local thermodynamic equilibrium, explicit expressions for the temperature and the chemical potentials in terms of the electromagnetic fields are obtained. The linear phenomenological relations describe novel effects of non-uniform electromagnetic fields on the transport equations and account also for magnetoresistance and optical tweezers.