Editing Irreversible process (section)

==History==
The German physicist [[Rudolf Clausius]], in the 1850s, was the first to mathematically quantify the discovery of irreversibility in nature through his introduction of the concept of [[entropy]]. In his 1854 memoir "On a Modified Form of the Second Fundamental Theorem in the Mechanical Theory of Heat," Clausius states:

{{cquote|It may, moreover, happen that instead of a descending transmission of heat accompanying, in the one and the same process, the ascending transmission, another permanent change may occur which has the peculiarity of ''not being reversible'' without either becoming replaced by a new permanent change of a similar kind, or producing a descending transmission of heat.}}

Simply, Clausius states that it is impossible for a system to transfer heat from a cooler body to a hotter body. For example, a cup of hot coffee placed in an area of room temperature {{nowrap|(~72 °F)}} will transfer heat to its surroundings and thereby cool down with the temperature of the room slightly increasing (to {{nowrap|~72.3 °F}}). However, that same initial cup of coffee will never absorb heat from its surroundings, causing it to grow even hotter, with the temperature of the room decreasing (to {{nowrap|~71.7 °F}}). Therefore, the process of the coffee cooling down is irreversible unless extra energy is added to the system.

However, a paradox arose when attempting to reconcile microanalysis of a system with observations of its macrostate. Many processes are mathematically reversible in their microstate when analyzed using classical Newtonian mechanics. This paradox clearly taints microscopic explanations of macroscopic tendency towards equilibrium, such as [[James Clerk Maxwell]]'s 1860 argument that molecular collisions entail an equalization of temperatures of mixed gases.<ref>{{Cite journal | last1 = Gyenis | first1 = Balazs | doi = 10.1016/j.shpsb.2017.01.001 | title = Maxwell and the normal distribution: A colored story of probability, independence, and tendency towards equilibrium | journal = Studies in History and Philosophy of Modern Physics | volume = 57 | pages = 53–65 | year = 2017| arxiv = 1702.01411 | bibcode = 2017SHPMP..57...53G | s2cid = 38272381 }}</ref> From 1872 to 1875, [[Ludwig Boltzmann]] reinforced the statistical explanation of this paradox in the form of [[Boltzmann's entropy formula]], stating that an increase of the number of possible microstates a system might be in, will increase the entropy of the system, making it less likely that the system will return to an earlier state. His formulas quantified the analysis done by [[William Thomson, 1st Baron Kelvin]], who had argued that:<ref>{{cite journal |last1=Bishop |first1=R. C. |last2=Bohm |first2=A. |last3=Gadella |first3=M. |title=Irreversibility in quantum mechanics |journal=Discrete Dynamics in Nature and Society |date=2004 |volume=2004 |issue=1 |pages=75–83 |doi=10.1155/S1026022604401046 |citeseerx=10.1.1.576.7850 |doi-access=free }}</ref><ref>{{cite book |doi=10.1007/3-540-59158-3_31 |chapter=Microscopic reversibility and macroscopic behavior: Physical explanations and mathematical derivations |title=25 Years of Non-Equilibrium Statistical Mechanics |series=Lecture Notes in Physics |year=1995 |last1=Lebowitz |first1=Joel L. |volume=445 |pages=1–20 |isbn=978-3-540-59158-0 |s2cid=16589172 }}</ref>

{{cquote|The equations of motion in abstract dynamics are perfectly reversible; any solution of these equations remains valid when the time variable t is replaced by –t. On the other hand, physical processes are irreversible: for example, the friction of solids, conduction of heat, and diffusion. Nevertheless, the principle of dissipation of energy is compatible with a molecular theory in which each particle is subject to the laws of abstract dynamics.}}

Another explanation of irreversible systems was presented by French mathematician [[Henri Poincaré]]. In 1890, he published his first explanation of nonlinear dynamics, also called [[chaos theory]]. Applying chaos theory to the [[second law of thermodynamics]], the paradox of irreversibility can be explained in the errors associated with scaling from microstates to macrostates and the degrees of freedom used when making experimental observations. Sensitivity to initial conditions relating to the system and its environment at the microstate compounds into an exhibition of irreversible characteristics within the observable, physical realm.<ref>[http://www.tim-thompson.com/entropy2.html "The 2nd Law of Thermodynamics"].Page dated 2002-2-19. Retrieved on 2010-4-01.</ref>

[[Image:Adiabatic-irrevisible-state-change.svg|thumb|Irreversible [[Adiabatic Process|adiabatic process]]: If the cylinder is a perfect insulator, the initial top-left state cannot be reached anymore after it is changed to the one on the top-right. Instead, the state on the bottom left is assumed when going back to the original pressure because energy is converted into heat.]]