  Janus motors with chemically active and inactive hemispheres can operate only
under nonequilibrium conditions where detailed balance is broken by fluxes of
chemical species that establish a nonequilibrium state. A microscopic model for
reversible reactive collisions on a Janus motor surface is constructed and
shown to satisfy detailed balance. The model is used to study Janus particle
reactive dynamics in systems at equilibrium where generalized chemical rate
laws that include time-dependent rate coefficients with power-law behavior are
shown to describe reaction rates. While maintaining reversible reactions on the
Janus catalytic hemisphere, the system is then driven into a nonequilibrium
steady state by fluxes of chemical species that control the chemical affinity.
The statistical properties of the self-propelled Janus motor in this
nonequilibrium steady state are investigated and compared with predictions of a
fluctuating thermodynamics theory. The model has utility beyond the examples
presented here, since it allows one to explore various aspects of
nonequilibrium fluctuations in systems with self-diffusiophoretic motors from a
microscopic perspective.
