  During a de Sitter stage of expansion the spectator fields of different spin
are constrained by the critical density bound and by further requirements
determined by their specific physical nature. The evolution of spectator
electric fields in conformally flat background geometries is occasionally
concocted by postulating the existence of ad hoc currents but this apparently
innocuous trick violates the second law of thermodynamics. Such a problem
occurs, in particular, for those configurations (customarily employed for the
analysis of the Schwinger effect in four-dimensional de Sitter backgrounds)
leading to an electric energy density which is practically unaffected by the
expansion of the underlying geometry. The obtained results are compared with
more mundane situations where Joule heating develops in the early stages of a
quasi-de Sitter phase.
