Editing Entropy (section)

== History ==
[[File:Clausius.jpg|thumb|upright|[[Rudolf Clausius]] (1822–1888), originator of the concept of entropy]]
{{Main|History of entropy}}

In his 1803 paper ''Fundamental Principles of Equilibrium and Movement'', the French mathematician [[Lazare Carnot]] proposed that in any machine, the accelerations and shocks of the moving parts represent losses of ''moment of activity''; in any natural process there exists an inherent tendency towards the dissipation of useful energy. In 1824, building on that work, Lazare's son, [[Nicolas Léonard Sadi Carnot|Sadi Carnot]], published ''[[Reflections on the Motive Power of Fire]]'', which posited that in all heat-engines, whenever "[[caloric theory|caloric]]" (what is now known as heat) falls through a temperature difference, work or [[work (physics)|motive power]] can be produced from the actions of its fall from a hot to cold body. He used an analogy with how water falls in a [[water wheel]]. That was an early insight into the [[second law of thermodynamics]].<ref>{{cite web |url=http://scienceworld.wolfram.com/biography/CarnotSadi.html |title=Carnot, Sadi (1796–1832) |publisher=Wolfram Research |year=2007 |access-date=24 February 2010}}</ref> Carnot based his views of heat partially on the early 18th-century "Newtonian hypothesis" that both heat and light were types of indestructible forms of matter, which are attracted and repelled by other matter, and partially on the contemporary views of [[Count Rumford]], who showed in 1789 that heat could be created by friction, as when cannon bores are machined.<ref>{{Cite book |last=McCulloch |first=Richard, S. |title=Treatise on the Mechanical Theory of Heat and its Applications to the Steam-Engine, etc. |publisher=D. Van Nostrand |year=1876}}</ref> Carnot reasoned that if the body of the working substance, such as a body of steam, is returned to its original state at the end of a complete [[engine cycle]], "no change occurs in the condition of the working body".

The [[first law of thermodynamics]], deduced from the heat-friction experiments of [[James Joule]] in 1843, expresses the concept of energy and its [[conservation of energy|conservation]] in all processes; the first law, however, is unsuitable to separately quantify the effects of [[friction]] and [[dissipation]].{{citation needed|date=May 2023}}

In the 1850s and 1860s, German physicist [[Rudolf Clausius]] objected to the supposition that no change occurs in the working body, and gave that change a mathematical interpretation, by questioning the nature of the inherent loss of usable heat when work is done, e.g., heat produced by friction.<ref name="Clausius">{{Cite journal |last=Clausius |first=Rudolf |title=Über die bewegende Kraft der Wärme und die Gesetze, welche sich daraus für die Wärmelehre selbst ableiten lassen |language=de |year=1850 |doi=10.1002/andp.18501550306 |journal=Annalen der Physik |volume=155 |issue=3 |hdl=2027/uc1.$b242250 |bibcode=1850AnP...155..368C |pages=368–397 |hdl-access=free}} [On the Motive Power of Heat, and on the Laws which can be deduced from it for the Theory of Heat] : Poggendorff's ''Annalen der Physik und Chemie''.</ref> He described his observations as a dissipative use of energy, resulting in a ''transformation-content'' ({{lang|de|Verwandlungsinhalt}} in German), of a [[thermodynamic system]] or [[working body]] of [[chemical species]] during a change of [[thermodynamic state|state]].<ref name="Clausius" /> That was in contrast to earlier views, based on the theories of [[Isaac Newton]], that heat was an indestructible particle that had mass. Clausius discovered that the non-usable energy increases as steam proceeds from inlet to exhaust in a steam engine. From the prefix ''en-'', as in 'energy', and from the Greek word {{lang|el|τροπή}} [tropē], which is translated in an established lexicon as ''turning'' or ''change''<ref>Liddell, H. G., Scott, R. (1843/1978). A Greek–English Lexicon, revised and augmented edition, Oxford University Press, Oxford UK, {{ISBN|0198642148}}, pp.&nbsp;1826–1827.</ref> and that he rendered in German as {{lang|de|Verwandlung}}, a word often translated into English as ''transformation'', in 1865 Clausius coined the name of that property as ''entropy''.<ref name = "Clausius German">{{cite journal |last1=Clausius |first1=Rudolf |year=1865 |title=Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie (Vorgetragen in der naturforsch. Gesellschaft zu Zürich den 24. April 1865) |language=de |journal=Annalen der Physik und Chemie |volume=125 |issue=7 |pages=353–400 |doi=10.1002/andp.18652010702 |bibcode=1865AnP...201..353C |url=https://zenodo.org/record/1423700 |quote=Sucht man für ''S'' einen bezeichnenden Namen, so könnte man, ähnlich wie von der Gröſse ''U'' gesagt ist, sie sey der ''Wärme- und Werkinhalt'' des Körpers, von der Gröſse ''S'' sagen, sie sey der ''Verwandlungsinhalt'' des Körpers. Da ich es aber für besser halte, die Namen derartiger für die Wissenschaft wichtiger Gröſsen aus den alten Sprachen zu entnehmen, damit sie unverändert in allen neuen Sprachen angewandt werden können, so schlage ich vor, die Gröſse ''S'' nach dem griechischen Worte ἡ τροπή, die Verwandlung, die ''Entropie'' des Körpers zu nennen. Das Wort ''Entropie'' habei ich absichtlich dem Worte ''Energie'' möglichst ähnlich gebildet, denn die beiden Gröſsen, welche durch diese Worte benannt werden sollen, sind ihren physikalischen Bedeutungen nach einander so nahe verwandt, daſs eine gewisse Gleichartigkeit in der Benennung mir zweckmäſsig zu seyn scheint. |quote-page=390}}</ref> The word was adopted into the English language in 1868.

Later, scientists such as [[Ludwig Boltzmann]], [[Josiah Willard Gibbs]], and [[James Clerk Maxwell]] gave entropy a statistical basis. In 1877, Boltzmann visualized a probabilistic way to measure the entropy of an ensemble of [[ideal gas]] particles, in which he defined entropy as proportional to the [[natural logarithm]] of the number of microstates such a gas could occupy. The [[proportionality (mathematics)|proportionality constant]] in this definition, called the [[Boltzmann constant]], has become one of the defining universal constants for the modern [[International System of Units]] (SI). Henceforth, the essential problem in [[statistical thermodynamics]] has been to determine the distribution of a given amount of energy ''E'' over ''N'' identical systems. [[Constantin Carathéodory]], a Greek mathematician, linked entropy with a mathematical definition of irreversibility, in terms of trajectories and integrability.