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RESEARCH PRODUCT

Geometric Aspects of Thermodynamics

Florian Scheck

subject

media_common.quotation_subjectEuclidean geometryExterior derivativeThermodynamicsDifferential calculusVector fieldSecond law of thermodynamicsCanonical transformationTangent vectorDirectional derivativeMathematicsmedia_common

description

This chapter deals with mathematical aspects of thermodynamics most of which will be seen to be primarily of geometrical nature. Starting with a short excursion to differentiable manifolds we summarize the properties of functions, of vector fields and of one-forms on thermodynamic manifolds. This summary centers on exterior forms over Euclidean spaces and the corresponding differential calculus. In particular, one-forms provide useful tools for the analysis of thermodynamics. A theorem by Caratheodory is developed which is closely related to the second law of thermodynamics. The chapter closes with a discussion of systems which depend on two variables and for which there is an interesting analogy to classical mechanics.

yearjournalcountryeditionlanguage
2016-01-01
https://doi.org/10.1007/978-3-319-40049-5_3