Thermodynamic stability of equilibrium system and critical state

On the basis of general Gibbs conditions of stability, the requirements of critical state stability that are applied to adiabatic coefficient of stability (ACS) and their derivatives are obtained. The examination of these conditions with critical state definition establishes the existence of four alternative types of critical behaviour of the thermodynamic system. These types are classified by the critical behaviour of ACS and K_C, which is connected with ACS. Analysis of the asymptotic behaviour of adiabatic quantity (AQ), which is consistent with stability requirements, demonstrates that both analytic and nonanalytic behaviours are possible.