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Geometrothermodynamic Cosmology.

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Geometrothermodynamics unifies geometry and thermodynamics, handling Legendre transformations geometrically. This formalism generates cosmological models from fundamental equations, explaining cosmic inflation and standard cosmology.

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Area of Science:

  • Thermodynamics
  • Differential Geometry
  • Cosmology

Background:

  • Classical thermodynamics relies on Legendre transformations for potential invariance.
  • Geometric formalisms offer new perspectives on thermodynamic systems.
  • Relativistic cosmology seeks fundamental equations to describe the universe.

Purpose of the Study:

  • To review and elaborate on the geometrothermodynamics formalism.
  • To demonstrate its application in handling thermodynamic potential invariance.
  • To show its utility in generating cosmological models via variational principles.

Main Methods:

  • Utilizing contact and Riemannian geometry to model thermodynamic systems.
  • Applying geometric methods to analyze Legendre invariance.
  • Employing variational principles to derive fundamental thermodynamic equations.

Main Results:

  • Geometrothermodynamics geometrically handles Legendre transformations, ensuring potential independence.
  • A variational principle within this formalism generates fundamental equations.
  • These equations can be applied to relativistic cosmology, yielding models with arbitrary parameters.

Conclusions:

  • Geometrothermodynamics provides a powerful geometric framework for thermodynamics.
  • The formalism successfully generates cosmological models, including those matching inflationary and standard paradigms.
  • This approach offers a unified perspective on thermodynamics and cosmology.