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Area of Science:

  • Thermodynamics
  • Electromagnetism
  • Statistical Mechanics

Background:

  • Defining work done on electromagnetic fields (EMF) is problematic due to non-gauge-invariant standard Hamiltonians, limiting statistical mechanics applications.
  • The first law of thermodynamics typically defines work via the time derivative of the Hamiltonian, which is not applicable here.

Purpose of the Study:

  • To derive a gauge-invariant Hamiltonian for EMFs dependent on physical observables.
  • To establish a framework for defining thermodynamic work and formulating the second law for EMFs.
  • To explore the connection between thermodynamic laws and the electrodynamic arrow of time.

Main Methods:

  • Developed a new, explicitly gauge-invariant Hamiltonian for the electromagnetic field.
  • Formulated definitions for thermodynamic work and the second law applicable to EMFs.
  • Investigated the implications for the electrodynamic arrow of time and photon mass.

Main Results:

  • Obtained a gauge-invariant Hamiltonian solely dependent on physical observables.
  • Successfully defined thermodynamic work and formulated the second law for EMFs.
  • Established a direct link between the second law for EMFs and the choice of retarded solutions (electrodynamic arrow of time).

Conclusions:

  • The new Hamiltonian resolves the issue of defining work on EMFs.
  • The formulation of the second law for EMFs provides new insights into thermodynamics and electromagnetism.
  • Thermodynamic work measurements using this framework may help determine if photons have a small, non-zero mass.