  Important models of nonequilibrium statistical physics (NESP) are limited by
a commonly used, but often unrecognized, near-equilibrium approximation.
Fokker-Planck and Langevin equations, the Einstein and random-flight diffusion
models, and the Schnakenberg model of biochemical networks suppose that
fluctuations are due to an ideal equilibrium bath. But far from equilibrium,
this perfect bath concept does not hold. A more principled approach should
derive the rate fluctuations from an underlying dynamical model, rather than
assuming a particular form. Here, using Maximum Caliber as the underlying
principle, we derive corrections for NESP processes in an imperfect - but more
realistic - environment, corrections which become particularly important for a
system driven strongly away from equilibrium. Beyond characterizing a heat bath
by the single equilibrium property of its temperature, the bath's speed and
size must also be used to characterize the bath's ability to handle fast or
large fluctuations.
