Para-Sasakian geometry in thermodynamic fluctuation theory

Abstract

In this work we tie concepts derived from statistical mechanics, information theory and contact Riemannian geometry within a single consistent formalism for thermodynamic fluctuation theory. We derive the concrete relations characterizing the geometry of the Thermodynamic Phase Space stemming from the relative entropy and the Fisher-Rao information matrix. In particular, we show that the Thermodynamic Phase Space is endowed with a natural para-contact pseudo-Riemannian structure derived from a statistical moment expansion which is para-Sasaki and η-Einstein. Moreover, we prove that such manifold is locally isomorphic to the hyperbolic Heisenberg group. In this way we show that the hyperbolic geometry and the Heisenberg commutation relations on the phase space naturally emerge from classical statistical mechanics. Finally, we argue on the possible implications of our results.

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References in corpus (2)

• Geometrothermodynamics
• The geometry of thermodynamic control

Cited by in corpus (5)

• Liouville's Theorem and the canonical measure for nonconservative systems from contact geometry
• Contact Geometry in Superconductors and New Massive Gravity
• Contact polarizations and associated metrics in geometric thermodynamics
• Maximally Symmetric Spacetimes emerging from thermodynamic fluctuations
• Gravitational Waves from Thurston Geometries