Editing Thermodynamics (section)

== Axiomatic thermodynamics ==

Axiomatic thermodynamics is a [[mathematical discipline]] that aims to describe thermodynamics in terms of rigorous [[axiom]]s, for example by finding a mathematically rigorous way to express the familiar [[laws of thermodynamics]].

The first attempt at an axiomatic theory of thermodynamics was [[Constantin Carathéodory]]'s 1909 work ''Investigations on the Foundations of Thermodynamics'', which made use of [[Integrability conditions for differential systems|Pfaffian systems]] and the concept of [[adiabatic accessibility]], a notion that was introduced by Carathéodory himself.<ref>{{Cite journal|last=Carathéodory|first=C.|date=1909|title=Untersuchungen über die Grundlagen der Thermodynamik|url=http://link.springer.com/10.1007/BF01450409|journal=[[Mathematische Annalen]]|language=de|volume=67|issue=3|pages=355–386|doi=10.1007/BF01450409|s2cid=118230148 |issn=0025-5831|via=}}</ref><ref name=frankel>{{cite book|last=Frankel |first=Theodore |title=The Geometry of Physics: An Introduction |edition=second |publisher=Cambridge University Press |year=2004 |isbn=9780521539272}}</ref> In this formulation, thermodynamic concepts such as [[heat]], [[entropy]], and [[temperature]] are derived from quantities that are more directly measurable.<ref>{{Cite journal|last=Rastall|first=Peter|date=1970-10-01|title=Classical Thermodynamics Simplified|url=https://aip.scitation.org/doi/10.1063/1.1665080|journal=[[Journal of Mathematical Physics]]|volume=11|issue=10|pages=2955–2965|doi=10.1063/1.1665080|bibcode=1970JMP....11.2955R |issn=0022-2488}}</ref> Theories that came after, differed in the sense that they made assumptions regarding [[thermodynamic process]]es with arbitrary initial and final states, as opposed to considering only neighboring states.