Geometric foundations of thermodynamics in the quantum regime

• URL: http://arxiv.org/abs/2511.10125v1
• Date: Fri, 14 Nov 2025 01:33:51 GMT
• Title: Geometric foundations of thermodynamics in the quantum regime
• Authors: Álvaro Tejero, Martín de la Rosa,
• Abstract summary: We present a comprehensive geometrical formulation of quantum thermodynamics based on contact geometry and principal fiber bundles.<n>A principal fiber bundle over the manifold of density operators distinguishes the quantum state structure from thermodynamic labels.<n>Non-equilibrium extensions, formulated through pseudo-Riemannian metrics and connections on the principal bundle, introduce curvature-induced holonomy that quantifies irreversibility in cyclic processes.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work, we present a comprehensive geometrical formulation of quantum thermodynamics based on contact geometry and principal fiber bundles. The quantum thermodynamic state space is modeled as a contact manifold, with equilibrium Gibbs states forming a Legendrian submanifold that encodes the fundamental thermodynamic relations. A principal fiber bundle over the manifold of density operators distinguishes the quantum state structure from thermodynamic labels: its fibers represent non-equilibrium configurations, and their unique intersections with the equilibrium submanifold enforce thermodynamic consistency. Quasistatic processes correspond to minimizing geodesics under the Bures-Wasserstein metric, leading to minimal dissipation, while the divergence of geodesic length toward rank-deficient states geometrically derives the third law. Non-equilibrium extensions, formulated through pseudo-Riemannian metrics and connections on the principal bundle, introduce curvature-induced holonomy that quantifies irreversibility in cyclic processes. In this framework, the thermodynamic laws in the quantum regime emerge naturally as geometric consequences.

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