We study a classical many-particle system with an external control represented by a time-dependent extensive parameter in a Lagrangian. We show that thermodynamic entropy of the system is uniquely characterized as the Noether invariant associated with a symmetry for an infinitesimal non-uniform time translation $t\to t+\eta\hbar \beta$, where $\eta$ is a small parameter, $\hbar$ is the Planck cons