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In a function which describes the system's potential energy, the system's equilibria can be determined using calculus.A system is in mechanical equilibrium at the critical points of the function describing the system's potential energy.
Mechanical equilibrium: If at every point within a given system there is no change in pressure with time, and there is no movement of material, the system is in mechanical equilibrium. Phase equilibrium : This occurs when the mass for each individual phase reaches a value that does not change with time.
In contrast, mechanical work and heat are process quantities or path functions because their values depend on a specific "transition" (or "path") between two equilibrium states that a system has taken to reach the final equilibrium state. Exchanged heat (in certain discrete amounts) can be associated with changes of state function such as enthalpy.
M. Zemansky also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium". [36] P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses ...
The grand canonical partition function applies to a grand canonical ensemble, in which the system can exchange both heat and particles with the environment, at fixed temperature, volume, and chemical potential. Other types of partition functions can be defined for different circumstances; see partition function (mathematics) for
Statistical equilibrium occurs if, for each state in the ensemble, the ensemble also contains all of its future and past states with probabilities equal to the probability of being in that state. (By contrast, mechanical equilibrium is a state with a balance of forces that has ceased to evolve.) The study of equilibrium ensembles of isolated ...
An equilibrium state is mathematically ascertained by seeking the extrema of a thermodynamic potential function, whose nature depends on the constraints imposed on the system. For example, a chemical reaction at constant temperature and pressure will reach equilibrium at a minimum of its components' Gibbs free energy and a maximum of their entropy.
Although a mechanical system certainly evolves over time, the ensemble does not necessarily have to evolve. In fact, the ensemble will not evolve if it contains all past and future phases of the system. Such a statistical ensemble, one that does not change over time, is called stationary and can be said to be in statistical equilibrium. [2]