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Thermodynamics had been a subject dear to Carathéodory since his time in Belgium. [19] In 1909, he published a pioneering work "Investigations on the Foundations of Thermodynamics" [20] in which he formulated the second law of thermodynamics axiomatically, that is, without the use of Carnot engines and refrigerators and only by mathematical ...
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] [3] It was also used by R. Giles in his 1964 monograph. [4]
Thermodynamics is a branch of physics that deals with heat, work, ... Constantin Carathéodory presented a purely mathematical approach in an axiomatic formulation, ...
The second law of thermodynamics may be expressed in many specific ways, [25] the most prominent classical statements [26] being the statement by Rudolf Clausius (1854), the statement by Lord Kelvin (1851), and the statement in axiomatic thermodynamics by Constantin Carathéodory (1909). These statements cast the law in general physical terms ...
Constantin Carathéodory proved in 1907 that if = + + +.is a holomorphic function on the unit disk D with positive real part, then [2] [3] | | In fact it suffices to show the result with g replaced by g r (z) = g(rz) for any r < 1 and then pass to the limit r = 1.
The idea is that it is possible to build a pre-measure on a semi-ring (for example Stieltjes measures), which can then be extended to a pre-measure on (), which can finally be extended to a measure on a σ-algebra through Caratheodory's extension theorem. As σ-algebras generated by semi-rings and rings are the same, the difference does not ...
The first law of thermodynamics is a formulation of the law of conservation of energy in the context of thermodynamic processes.The law distinguishes two principal forms of energy transfer, heat and thermodynamic work, that modify a thermodynamic system containing a constant amount of matter.
Given a set , let denote the collection of all subsets of , including the empty set. An outer measure on is a set function: [,] such that . null empty set ...