Adiabatic Accessibility Information
Adiabatic accessibility denotes a certain relation between two equilibrium states of a thermodynamic system (or of different such systems). The concept was coined by Constantin Carathéodory[1] in 1909 ("adiabatische Erreichbarkeit") and taken up 90 years later by Elliott Lieb and J. Yngvason in their axiomatic approach to the foundations of thermodynamics [2]. It was also used by R. Giles in his 1964 monograph. [3]
The original definition of Carathéodory was limited to reversible, quasistatic process, described by a curve in the manifold of equilibrium states of the system under consideration. He called such a state change adiabatic if the infinitesimal 'heat' differential form vanishes along the curve. In other words, at no time in the process does heat enter or leave the system. Carathéodory's formulation of the Second Law of Thermodynamics then takes the form: "In the neighbourhood of any initial state, there are states which cannot be approached arbitrarily close through adiabatic changes of state." From this principle he derived the existence of entropy as a state function S whose differential dS is proportional to the heat differential form δQ, so it remains constant under adiabatic state changes (in Carathéodory's sense). The increase of entropy during irreversible processes is not obvious in this formulation, without further assumptions.
The definition employed by Lieb and Yngvason is rather different since the state changes considered can be the result of arbitrarily complicated, possibly violent, irreversible processes and there is no mention of 'heat' or differential forms. It goes as follows: A state Y is adiabatically accessible from a state X, in symbols , if it is possible to transform X into Y in such a way that the only net effect of the process on the surroundings is that a weight has been raised or lowered (or a spring is stretched/compressed, or a flywheel is set in motion).
A definition of thermodynamic entropy can be based entirely on certain properties of the relation of adiabatic accessibility that are taken as axioms in the Lieb-Yngvason approach. The entropy has the property that if and only if , in accord with the Second Law.
Sources
- ^ Constantin Carathéodory: Untersuchungen über die Grundlagen der Thermodynamik, Math. Ann., 67:355–386, 1909
- ^ Elliott H. Lieb, Jakob Yngvason: The Physics and Mathematics of the Second Law of Thermodynamics, Phys. Rep. 310, 1-96 (1999)
- ^ Robin Giles: "Mathematical Foundations of Thermodynamics", Pergamon, Oxford 1964
References
- E.H. Lieb, J. Yngvason "The Entropy of Classical Thermodynamics", in `Entropy', pp.\ 147—193, A. Greven. G. Keller and G. Warnecke, Eds., Princeton Series in Applied Mathematics, Princeton University Press, 2003
- André Thess: Das Entropieprinzip - Thermodynamik für Unzufriedene, Oldenbourg-Verlag 2007, ISBN 978-3-486-58428-8. English Version: The Entropy Principle - Thermodynamics for the Unsatisfied, Springer-Verlag 2011.
External links
- A. Thess: (German)
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