# Thermodynamic Stability

## Stability, Thermodynamic

stability of the thermodynamic equilibrium of a system relative to small variations in the system’s thermodynamic parameters, such as volume, pressure, and temperature.

In the general case a state of equilibrium is characterized by the minimum value of a thermodynamic potential that corresponds to variables that are independent under the conditions of the experiment. For example, when the entropy, volume, and number of moles of components are independent variables, the system’s internal energy *U* must be minimal if the system is to be in thermodynamic equilibrium. It follows from this requirement that the first variation δ*U* must be equal to zero under small variations of the variables and at constant total entropy, volume, and number of particles. Constancy of temperature and pressure for all phases and equality of the values of the chemical potential for each of the components in coexisting phases follow from this fact, as an equilibrium condition. Even when these conditions are fulfilled, there is no assurance of thermodynamic stability of the system. Still another condition—a positive value of the second variation of δ^{2}*U*—follows from the condition of minimum *U*. This leads to a number of thermodynamic inequalities, which are the conditions of thermodynamic stability. For example, one such condition is a positive value of the heat capacity of the system at constant volume; another is decreasing pressure with increasing volume at constant temperature.

In the general case, thermodynamic stability may be stated as the following principle: an external influence that removes a system from a state of equilibrium induces in that system processes that tend to counteract the effect of the influence (*see*LE CHATELIER’S PRINCIPLE). A complete theory of thermodynamic stability for both homogeneous and heterogeneous systems was developed in the late 19th century by J. W. Gibbs.

Metastable equilibrium may also have the property of thermodynamic equilibrium to some extent. Although metastable equilibrium corresponds to minimum internal energy or the minimum of some other thermodynamic potential, this minimum lies above the principal minimum, which defines the most stable state (*see*METASTABLE STATE).

D. N. ZUBAREV