  In classical Maxwell electrodynamics, charged particles following
deterministic trajectories are described by currents that induce fields,
mediating interactions with other particles. Statistical methods are used when
needed to treat complex particle and/or field configurations. In
Stueckelberg-Horwitz-Piron (SHP) electrodynamics, the classical trajectories
are traced out dynamically, through the evolution of a 4D spacetime event
$x^\mu (\tau)$ as $\tau$ grows monotonically. Stueckelberg proposed to
formalize the distinction between coordinate time $x^0 = ct$ (measured by
laboratory clocks) and chronology $\tau$ (the temporal ordering of event
occurrence) in order to describe antiparticles and resolve problems of
irreversibility such as grandfather paradoxes. Consequently, in SHP theory, the
elementary object is not a particle (a 4D curve in spacetime) but rather an
event (a single point along the dynamically evolving curve). Following standard
deterministic methods in classical relativistic field theory, one is led to
Maxwell-like field equations that are \hbox{$\tau$-dependent} and sourced by a
current that represents a statistical ensemble of instantaneous events
distributed along the trajectory. The width $\lambda$ of this distribution
defines a correlation time for the interactions and a mass spectrum for the
photons emitted by particles. As $\lambda$ becomes very large, the photon mass
goes to zero and the field equations become $\tau$-independent Maxwell's
equations. Maxwell theory thus emerges as an equilibrium limit of SHP, in which
$\lambda$ is larger than any other relevant time scale. Thus, statistical
mechanics is a fundamental ingredient in SHP electrodynamics, and its insights
are required to give meaning to the concept of a particle.
