Thermodynamic Equilibrium

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Systemsin 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, until 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),[2] 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):

Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.

Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability.[3] When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.

A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.

A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium.[5][6] (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics.[7] One textbook[8] calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition, which apparently was suggested by Fowler.)

Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.

The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.

If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy.[9][10][11][12] Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.

A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process.[13] It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings.[14][15] The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.[16]

It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.

It can be useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.

If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.

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