  We assume that markovian dynamics on a finite graph enjoys a gauge symmetry
under local scalings of the probability density, derive the transformation law
for the transition rates and interpret the thermodynamic force as a gauge
potential. A widely accepted expression for the total entropy production of a
system arises as the simplest gauge-invariant completion of the time derivative
of Gibbs's entropy. We show that transition rates can be given a simple
physical characterization in terms of locally-detailed-balanced heat
reservoirs. It follows that Clausius's measure of irreversibility along a
cyclic transformation is a geometric phase. In this picture, the gauge symmetry
arises as the arbitrariness in the choice of a prior probability. Thermostatics
depends on the information that is disposable to an observer; thermodynamics
does not.
