Thermodynamic equilibrium

Thermodynamic equilibrium is a notion of thermodynamics with axiomatic status referring to an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium, there are no net macroscopic flows of mass nor of energy within a system or between systems. In a system that is in its own state of internal thermodynamic equilibrium, not only is there an absence of macroscopic change, but there is an "absence of any tendency toward change on a macroscopic scale."

Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, while not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, unless disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium.

A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.

In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a "meta-stable equilibrium".

Though not a widely named "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when an isolated body of material starts from an equilibrium state, in which portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable, then it spontaneously reaches its own new state of internal thermodynamic equilibrium and this is accompanied by an increase in the sum of the entropies of the portions.

Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized (in the absence of an applied voltage), or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a closed system at constant volume and temperature (controlled by a heat bath):

Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a closed system at constant temperature and pressure, both controlled by the surroundings:

where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system. In other words, ${\displaystyle \Delta G=0}$ is a necessary condition for chemical equilibrium under these conditions (in the absence of an applied voltage).