Geometric Quantum Thermodynamics

Fabio Anza and James P. Crutchfield

Complexity Sciences Center
Physics Department
University of California at Davis
Davis, CA 95616

ABSTRACT: Building on parallels between geometric quantum mechanics and classical mechanics, we explore an alternative basis for quantum thermodynamics that exploits the differential geometry of the underlying state space. We develop both microcanonical and canonical ensembles, introducing continuous mixed states as distributions on the manifold of quantum states. We call out the ex- perimental consequences for a gas of qudits. We define quantum heat and work in an intrinsic way, including single-trajectory work, and reformulate thermodynamic entropy in a way that accords with classical, quantum, and information-theoretic entropies. We give both the First and Second Laws of Thermodynamics and Jarzynki's Fluctuation Theorem. The result is a more transparent physics, than conventionally available, in which the mathematical structure and physical intuitions underlying classical and quantum dynamics are seen to be closely aligned.

Fabio Anza and James P. Crutchfield, “Geometric Quantum Thermodynamics”, (2020).
[pdf]. [quant-phys].