In this contribution, we carry on with the research program initiated in J. Math. Chem., 58(6), 2020. Using the methods from geometric thermodynamics, we formally derive and analyze different conditions for thermodynamic stability and determine the limits of their use. In particular, we study, in detail, several versions of the Le Chatelier-Brown principle and demonstrate their application to the analysis of thermodynamic stability.
Keywords: Gibbs stability condition; Le Chatelier— Brown principle; equilibrium thermodynamics; geometric thermodynamics; implicit function theorem; stability condition.