Geometry of restricted information: the case of quantum thermodynamics

TL;DR

This paper introduces a geometric framework for quantum thermodynamics based on gauge symmetries representing measurement constraints, unifying thermodynamic laws through invariant quantities and revealing irreversibility as a geometric effect.

Contribution

It develops a gauge-invariant geometric approach to quantum thermodynamics that generalizes traditional energy-based thermodynamics to include arbitrary information constraints.

Findings

Invariant entropy satisfies a fluctuation theorem

Derived a Clausius-like inequality unifying thermodynamic laws

Entropy production linked to irreversibility as a geometric property

Abstract

We formulate a geometric framework in which physical laws emerge from restricted access to microscopic information. Measurement constraints are modeled as a gauge symmetry acting on density operators, inducing a gauge-reduced space of physically distinguishable states. In the case of quantum thermodynamics, this construction leads to a gauge-invariant formulation in which the invariant entropy admits a stochastic description and satisfies a general detailed fluctuation theorem. From this result, we derive an integrated fluctuation theorem and a Clausius-like inequality that unifies the first and second laws in terms of invariant work and coherent heat. Entropy production is identified with the relative entropy between forward and backward probability measures on the gauge-reduced space of thermodynamic trajectories, revealing irreversibility as a geometric consequence of limited observability. The third law emerges as a singular zero-temperature limit in which thermodynamic orbits collapse and entropy production vanishes. Since the framework applies to arbitrary information constraints, it encompasses energy-based thermodynamics as a particular case of more general measurement scenarios.