  "Ceci n'est pas une pipe" wrote Ren\'e Magritte on what was only the
representation of a pipe. Phenomena and their physical descriptions differ, and
in particular the laws ruling the former might enjoy symmetries that have to be
spent to attain the latter. So, inertial frames are necessary to draw numbers
out of Newtonian mechanics and confront with experiment, but ultimately the
laws of mechanics are independent of reference frames. Generalizing work done
in Ref. [M. Polettini, EPL 97 (2012) 30003] to continuous systems, we discuss
from a foundational point of view how subjectivity in the choice of reference
prior probability is a (gauge) symmetry of thermodynamics. In particular, a
change of priors corresponds to a change of coordinates. Employing an approach
based on the stochastic thermodynamics of continuous state-space diffusion
processes, we discuss the difference between thermostatic and thermodynamic
observables and show that, while the quantification of entropy depends on
priors, the second law of thermodynamics is formulated in terms of invariant
quantities, in particular the curvature of the thermodynamic force (gauge
potential), which we calculate in a few examples of processes led by different
nonequilibrium mechanisms.
