Carathéodory’s formulation of the second law of thermodynamics

E118707

axiomatic formulation formulation of physical law thermodynamic principle

Carathéodory’s formulation of the second law of thermodynamics is a mathematically rigorous restatement of the second law based on the inaccessibility of certain thermodynamic states, providing a foundation for the concept of entropy without relying on cyclic processes or heat engines.

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All labels observed (1)

Label	Occurrences
Carathéodory’s formulation of the second law of thermodynamics canonical	1

Statements (47)

Predicate	Object
instanceOf	axiomatic formulation ⓘ formulation of physical law ⓘ thermodynamic principle ⓘ
addresses	existence of entropy without statistical mechanics ⓘ integrability of the heat differential ⓘ
appliesTo	equilibrium thermodynamics of closed systems ⓘ simple compressible systems ⓘ
assumes	continuity of state variables ⓘ differentiability of thermodynamic functions ⓘ equilibrium thermodynamic states ⓘ
author	Constantin Carathéodory ⓘ
avoids	assumption of cyclic processes ⓘ explicit reference to Carnot cycles ⓘ explicit reference to heat engines ⓘ
basedOn	adiabatic inaccessibility ⓘ inaccessibility of states ⓘ
characteristic	geometric viewpoint on thermodynamics ⓘ local formulation of the second law ⓘ mathematical rigor ⓘ
clarifies	conditions for existence of entropy as state function ⓘ relationship between heat and work in reversible processes ⓘ
coreStatement	In every neighborhood of any state there exist states that are adiabatically inaccessible from it ⓘ
defines	entropy up to an integrating factor ⓘ
equivalentTo	traditional second law for simple systems under suitable assumptions ⓘ
field	mathematical physics ⓘ statistical mechanics ⓘ thermodynamics ⓘ
formalismType	differential geometric ⓘ
implies	dQ = T dS for quasi-static processes ⓘ existence of absolute temperature T as integrating factor ⓘ existence of entropy function S ⓘ
influenced	geometric formulations of thermodynamics ⓘ modern axiomatic thermodynamics ⓘ
languageOfOriginalPublication	German ⓘ
partOf	second law of thermodynamics ⓘ
provides	foundation for entropy without cyclic processes ⓘ foundation for entropy without heat engines ⓘ
publishedIn	Mathematische Annalen ⓘ
relatesTo	Clausius formulation of the second law ⓘ Kelvin–Planck statement of the second law of thermodynamics ⓘ surface form: Kelvin–Planck formulation of the second law
usesConcept	Pfaffian form ⓘ adiabatic process ⓘ exact differential ⓘ integrating factor ⓘ state space ⓘ thermodynamic manifold ⓘ
yearProposed	1909 ⓘ

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Subject: Carathéodory’s formulation of the second law of thermodynamics
Description of subject: Carathéodory’s formulation of the second law of thermodynamics is a mathematically rigorous restatement of the second law based on the inaccessibility of certain thermodynamic states, providing a foundation for the concept of entropy without relying on cyclic processes or heat engines.

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

Constantin Carathéodory → notableWork → Carathéodory’s formulation of the second law of thermodynamics ⓘ