Adiabatic accessibility

Adiabatic accessibility describes a relation between different states of a thermodynamic system. The term "adiabatic accessibility" coined by Constantin Carathéodory in 1909 was taken up in 1999 by Elliott Lieb and Jakob Yngvason as part of their axiomatic foundation of thermodynamics . With the help of the concept of adiabatic accessibility, the entropy can be defined without using the concepts of “heat” or “temperature” and without using information about the microscopic structure of matter.

A state Y of a thermodynamic system is described as adiabatically attainable starting from state X of the same system , if it is possible to transfer the system from state X to state Y with the aid of an "apparatus" and a weight within the framework of a process, whereby at the end of the process the apparatus returns to the state it was in at the beginning of the process. The weight may have changed its position in the gravitational field.

If, for example, the system is a certain amount of water, in state X the water is in the form of snow and in state Y in liquid form, then Y can be reached adiabatically from X. You then write , spoken, "X is before Y". For example, a weight on a thread can drive a mechanical stirrer via a roller from which the thread is unwound, which causes the snow to melt. Conversely, X cannot be reached adiabatically from Y, which is summarized with the notation (“X is really before Y”). ${\ displaystyle X \ prec Y}$ ${\ displaystyle X \ prec \ prec Y}$

Two states that are mutually achievable adiabatically are called adiabatically equivalent .

The entropy is then defined within the framework of the Lieb-Yngvason theory as a function of the system state in such a way that

the entropy of two states is equal if and only if they are adiabatically equivalent;
the entropy of state X is smaller than that of state Y if and only if Y can be reached adiabatically from X, but not vice versa.

literature

Elliott H. Lieb (editors: B. Nachtergaele, JP Solovej, J. Yngvason): Statistical Mechanics: Selecta of Elliott H. Lieb . 2005, ISBN 978-3-540-22297-2
André Thess: The entropy principle - thermodynamics for the dissatisfied . Oldenbourg-Verlag, 2007, ISBN 978-3-486-58428-8

Web links

A. Thess: What is entropy? An answer for the dissatisfied . (PDF; 249 kB) Publication manuscript

Individual evidence

↑ Constantin Carathéodory: Investigations on the fundamentals of thermodynamics , Math. Ann. , 67: 355-386, 1909.
^ Elliott H. Lieb, Jakob Yngvason: The Physics and Mathematics of the Second Law of Thermodynamics . In: Phys. Rep. , 310, 1999, pp. 1-96 arxiv : cond-mat / 9708200 .
↑ For earlier use of the term see W. Muschik: Aspects of Non-Equilibrium Thermodynamics: Six Lectures on Fundamentals and Methods . 1990. Wassim M. Haddad, VijaySekhar Chellaboina and Sergey G. Nersesov refer in Thermodynamics: A Dynamical Systems Approach (2005) to Constantin Carathéodory as one of the founders of axiomatic thermodynamics . Carathéodory's 1909 publication ( First axiomatically strict justification of thermodynamics ) received great attention from Max Planck and Max Born .

[1] Constantin Carathéodory: Investigations on the fundamentals of thermodynamics , Math. Ann. , 67: 355-386, 1909.

[2] Elliott H. Lieb, Jakob Yngvason: The Physics and Mathematics of the Second Law of Thermodynamics . In: Phys. Rep. , 310, 1999, pp. 1-96 arxiv : cond-mat / 9708200 .

[3] For earlier use of the term see W. Muschik: Aspects of Non-Equilibrium Thermodynamics: Six Lectures on Fundamentals and Methods . 1990. Wassim M. Haddad, VijaySekhar Chellaboina and Sergey G. Nersesov refer in Thermodynamics: A Dynamical Systems Approach (2005) to Constantin Carathéodory as one of the founders of axiomatic thermodynamics . Carathéodory's 1909 publication ( First axiomatically strict justification of thermodynamics ) received great attention from Max Planck and Max Born .