  We propose a Langevin equation for systems in an environment with nonuniform
temperature. At odds with an older proposal, ours admits a locally Maxwellian
steady state, local equipartition holds and for detailed-balanced (reversible)
systems statistical and physical entropies coincide. We describe its
thermodynamics, which entails a generalized version of the First Law and
Clausius's characterization of reversibility. Finally, we show that a Brownian
particle constrained into a smooth curve behaves according to our equation, as
if experiencing nonuniform temperature.
