Le Chatelier's principle

This principle describes the stability of a system in thermodynamic equilibrium.

Le Chatelier's principle: In response to small deviations away from equilibrium, the system will change in a manner that restores equilibrium.

This translates to conditions on the second derivatives of thermodynamic potentials such as entropy, $S(U,\ldots )$. For instance, the entropy is a concave function of its arguments such as internal energy. Thus, one has

${\frac {\partial ^{2}S}{\partial U^{2}}}\geq 0\ .$

Similarly, specific heats can be shown to be positive definite.