  We study the thermodynamic entropy as a Noether invariant in a stochastic
process. Following the Onsager theory, we consider the Langevin equation for a
thermodynamic variable in a thermally isolated system. By analyzing the
Martin-Siggia-Rose-Janssen-de Dominicis action of the Langevin equation, we
find that this action possesses a continuous symmetry in quasi-static
processes, which leads to the thermodynamic entropy as the Noether invariant
for the symmetry.
