  Entropy increase is fundamentally related to the breaking of time-reversal
symmetry. By adding the 'extra dimension' associated with thermodynamic forces,
we extend that discrete symmetry to a continuous symmetry for the dynamical
fluctuations around (nonlinear) gradient flow. The latter connects macroscopic
equilibrium conditions upon introducing a quasistatic protocol of control
parameters. The entropy state function becomes the Noether charge. As a result,
and following ideas expressed by Shin-ichi Sasa and co-workers, the adiabatic
invariance of the entropy, part of the Clausius heat theorem, gets connected
with the Noether theorem.
