Editing Second law of thermodynamics (section)

== Irreversibility ==
Irreversibility in [[thermodynamic process]]es is a consequence of the asymmetric character of thermodynamic operations, and not of any internally irreversible microscopic properties of the bodies. Thermodynamic operations are macroscopic external interventions imposed on the participating bodies, not derived from their internal properties. There are reputed "paradoxes" that arise from failure to recognize this.

=== Loschmidt's paradox ===
{{main|Loschmidt's paradox}}
[[Loschmidt's paradox]], also known as the reversibility paradox, is the objection that it should not be possible to deduce an irreversible process from the time-symmetric dynamics that describe the microscopic evolution of a macroscopic system.

In the opinion of Schrödinger, "It is now quite obvious in what manner you have to reformulate the law of entropy{{snd}}or for that matter, all other irreversible statements{{snd}}so that they be capable of being derived from reversible models. You must not speak of one isolated system but at least of two, which you may for the moment consider isolated from the rest of the world, but not always from each other."<ref>[[Erwin Schrödinger|Schrödinger, E.]] (1950), p.&nbsp;192.</ref> The two systems are isolated from each other by the wall, until it is removed by the thermodynamic operation, as envisaged by the law. The thermodynamic operation is externally imposed, not subject to the reversible microscopic dynamical laws that govern the constituents of the systems. It is the cause of the irreversibility. The statement of the law in this present article complies with Schrödinger's advice. The cause–effect relation is logically prior to the second law, not derived from it. This reaffirms Albert Einstein's postulates that cornerstone Special and General Relativity - that the flow of time is irreversible, however it is relative. Cause must precede effect, but only within the constraints as defined explicitly within [[General Relativity]] (or [[Special Relativity]], depending on the local spacetime conditions). Good examples of this are the [[Ladder paradox|Ladder Paradox]], [[time dilation]] and [[length contraction]] exhibited by objects approaching the velocity of light or within proximity of a super-dense region of mass/energy - e.g. black holes, neutron stars, magnetars and quasars.

=== Poincaré recurrence theorem ===
{{Main|Poincaré recurrence theorem}}
The [[Poincaré recurrence theorem]] considers a theoretical microscopic description of an isolated physical system. This may be considered as a model of a thermodynamic system after a thermodynamic operation has removed an internal wall. The system will, after a sufficiently long time, return to a microscopically defined state very close to the initial one. The Poincaré recurrence time is the length of time elapsed until the return. It is exceedingly long, likely longer than the life of the universe, and depends sensitively on the geometry of the wall that was removed by the thermodynamic operation. The recurrence theorem may be perceived as apparently contradicting the second law of thermodynamics. More obviously, however, it is simply a microscopic model of thermodynamic equilibrium in an isolated system formed by removal of a wall between two systems. For a typical thermodynamical system, the recurrence time is so large (many many times longer than the lifetime of the universe) that, for all practical purposes, one cannot observe the recurrence. One might wish, nevertheless, to imagine that one could wait for the Poincaré recurrence, and then re-insert the wall that was removed by the thermodynamic operation. It is then evident that the appearance of irreversibility is due to the utter unpredictability of the Poincaré recurrence given only that the initial state was one of thermodynamic equilibrium, as is the case in macroscopic thermodynamics. Even if one could wait for it, one has no practical possibility of picking the right instant at which to re-insert the wall. The Poincaré recurrence theorem provides a solution to Loschmidt's paradox. If an isolated thermodynamic system could be monitored over increasingly many multiples of the average Poincaré recurrence time, the thermodynamic behavior of the system would become invariant under time reversal.

=== Maxwell's demon ===
{{main|Maxwell's demon}}
[[File:James-clerk-maxwell3.jpg|thumb|upright|James Clerk Maxwell]]
[[James Clerk Maxwell]] imagined one container divided into two parts, ''A'' and ''B''. Both parts are filled with the same [[gas]] at equal temperatures and placed next to each other, separated by a wall. Observing the [[molecule]]s on both sides, an imaginary [[demon]] guards a microscopic trapdoor in the wall. When a faster-than-average molecule from ''A'' flies towards the trapdoor, the demon opens it, and the molecule will fly from ''A'' to ''B''. The average [[speed]] of the molecules in ''B'' will have increased while in ''A'' they will have slowed down on average. Since average molecular speed corresponds to temperature, the temperature decreases in ''A'' and increases in ''B'', contrary to the second law of thermodynamics.<ref name=":1">{{Cite web |title=Maxwell's demon {{!}} physics {{!}} Britannica |url=https://www.britannica.com/science/Maxwells-demon |access-date=2023-03-14 |website=www.britannica.com |language=en}}</ref>

One response to this question was suggested in 1929 by [[Leó Szilárd]] and later by [[Léon Brillouin]]. Szilárd pointed out that a real-life Maxwell's demon would need to have some means of measuring molecular speed, and that the act of acquiring information would require an expenditure of energy.<ref name=":2">{{Cite journal |last=Norton |first=John |date=3 July 2013 |title=All Shook Up: Fluctuations, Maxwell's Demon and the Thermodynamics of Computation |journal=Entropy |volume=15 |issue=12 |pages=4432–4483 |doi=10.3390/e15104432 |bibcode=2013Entrp..15.4432N |doi-access=free }}</ref> Likewise, Brillouin demonstrated that the decrease in entropy caused by the demon would be less than the entropy produced by choosing molecules based on their speed.<ref name=":1" />

Maxwell's 'demon' repeatedly alters the permeability of the wall between ''A'' and ''B''. It is therefore performing [[thermodynamic operation]]s on a microscopic scale, not just observing ordinary spontaneous or natural macroscopic thermodynamic processes.<ref name=":2" />