Differential Geometric Foundations of Non-Equilibrium Thermodynamics Formulation of the Three Laws of Thermodynamics on Composite Fibred Cocontact Phase Manifolds
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Beschreibung
Produktdetails
Einband
Gebundene Ausgabe
Erscheinungsdatum
19.02.2025
Verlag
BoD – Books on DemandSeitenzahl
444
Maße (L/B/H)
30,3/21,5/3,2 cm
Gewicht
1551 g
Auflage
1
Sprache
Englisch
ISBN
978-3-7693-1041-2
Some central results are the following: while in the theory of relativity the energy-momentum tensor determines the geometry of the space, in non-equilibrium thermodynamics, the 1-form of the entropy production rate is responsible for the emergence of a well-known geometric structure: the contact geometry. Relaxation processes remain in the fibers in which they start and end on an attractor manifold, that can be identified with the classical equilibrium subspace of thermostatics. One then proves, that outside this attractor manifold there are no reversible process directions. As a consequence of this, the 2nd Law of thermodynamics lives mainly on the fibers of the state manifold, the so called vertical geometric structure, while the 1st Law of thermodynamics is formulated on the horizontal components of the state manifold. The internal energy provides a physical gauge for each fiber. The 1st and 2nd Law of thermodynamics are coupled via the representation of the entropy flux 1-form that can be represented in the dual basis of exchange 1-forms such as the heat 1-form. This fact can be used to provide a "coordinate free" ("invariant") definition of non-equilibrium temperature. Finally, it is shown that probably the most general geometric structure to model non-equilibrium thermodynamics of compact (discrete Schottky systems) systems is given by a composite fibred cocontact phase manifold that includes time as an explicit dimension.
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