Defining work done on electromagnetic field

TL;DR

This paper introduces a gauge-invariant Hamiltonian for electromagnetic fields, enabling the definition of thermodynamic work and linking it to the electrodynamic arrow of time, with implications for photon mass measurement.

Contribution

A new gauge-invariant Hamiltonian for EMF is proposed, allowing thermodynamic analysis and connection to the arrow of time.

Findings

Hamiltonian depends only on physical observables

Enables defining work done on EMF thermodynamically

Links the second law to the electrodynamic arrow of time

Abstract

The problem of defining work done on electromagnetic field (EMF) via moving charges does not have a ready solution, because the standard Hamiltonian of EMF does not predict gauge-invariant energy changes. This limits applications of statistical mechanics to EMF. We obtained a new, explicitly gauge-invariant Hamiltonian for EMF that depends only on physical observables. This Hamiltonian allows to define thermodynamic work done on EMF and to formulate the second law for the considered situation. It also leads to a direct link between this law and the electrodynamic arrow of time, i.e. choosing retarded, and not advanced solutions of wave-equations. Measuring the thermodynamic work can give information on whether the photon mass is small but non-zero.