Editing Second law of thermodynamics (section)

== Non-equilibrium states ==
{{main|Non-equilibrium thermodynamics}}
The theory of classical or [[thermodynamic equilibrium|equilibrium thermodynamics]] is idealized. A main postulate or assumption, often not even explicitly stated, is the existence of systems in their own internal states of thermodynamic equilibrium. In general, a region of space containing a physical system at a given time, that may be found in nature, is not in thermodynamic equilibrium, read in the most stringent terms. In looser terms, nothing in the entire universe is or has ever been truly in exact thermodynamic equilibrium.<ref name="Grandy 151">Grandy, W.T. (Jr) (2008), p. 151.</ref><ref>Callen, H.B. (1960/1985), p. 15.</ref>

For purposes of physical analysis, it is often enough convenient to make an assumption of [[thermodynamic equilibrium]]. Such an assumption may rely on trial and error for its justification. If the assumption is justified, it can often be very valuable and useful because it makes available the theory of thermodynamics. Elements of the equilibrium assumption are that a system is observed to be unchanging over an indefinitely long time, and that there are so many particles in a system, that its particulate nature can be entirely ignored. Under such an equilibrium assumption, in general, there are no macroscopically detectable [[thermal fluctuations|fluctuations]]. There is an exception, the case of [[critical point (thermodynamics)|critical states]], which exhibit to the naked eye the phenomenon of [[critical opalescence]]. For laboratory studies of critical states, exceptionally long observation times are needed.

In all cases, the assumption of thermodynamic equilibrium, once made, implies as a consequence that no putative candidate "fluctuation" alters the entropy of the system.

It can easily happen that a physical system exhibits internal macroscopic changes that are fast enough to invalidate the assumption of the constancy of the entropy. Or that a physical system has so few particles that the particulate nature is manifest in observable fluctuations. Then the assumption of thermodynamic equilibrium is to be abandoned. There is no unqualified general definition of entropy for non-equilibrium states.<ref>Lieb, E.H., Yngvason, J. (2003), p. 190.</ref>

There are intermediate cases, in which the assumption of local thermodynamic equilibrium is a very good approximation,<ref>Gyarmati, I. (1967/1970), pp. 4-14.</ref><ref>Glansdorff, P., Prigogine, I. (1971).</ref><ref>[[Gottfried Wilhelm Leibniz Prize|Müller, I.]] (1985).</ref><ref>[[Gottfried Wilhelm Leibniz Prize|Müller, I.]] (2003).</ref> but strictly speaking it is still an approximation, not theoretically ideal.

For non-equilibrium situations in general, it may be useful to consider statistical mechanical definitions of other quantities that may be conveniently called 'entropy', but they should not be confused or conflated with thermodynamic entropy properly defined for the second law. These other quantities indeed belong to statistical mechanics, not to thermodynamics, the primary realm of the second law.

The physics of macroscopically observable fluctuations is beyond the scope of this article.