What thermodynamic condition must be met for a state of equilibrium to exist?

A thermodynamic system is said to be in a state of equilibrium when the macroscopic properties of the system, such as temperature, pressure and chemical composition, remain constant over time. It indicates that macroscopic properties are uniform throughout the system and there are no net flows of matter or energy within the system.

The basic thermodynamic condition for a system to be in a state of equilibrium is that its total entropy (S) must be maximized, or its total energy (U) must be minimized, while other macroscopic properties like volume (V), temperature (T), and the number of particles (N) in the system are kept constant. In mathematical terms, this can be expressed as: \(\left(\frac{\partial S}{\partial U}\right)_{V, N} = \frac{1}{T}\) (maximum entropy condition) or \(\left(\frac{\partial U}{\partial S}\right)_{V, N} = T\) (minimum energy condition) These conditions ensure that energy is distributed uniformly throughout the system and that there are no net flows of energy or matter, which means that the system is not changing and is in equilibrium.