Thermal pure state path integral and emergent symmetry

TL;DR

This paper develops a path integral framework using thermal pure states to analyze quantum many-body systems under external control, revealing an emergent symmetry and entropy invariance during quasi-static processes.

Contribution

It introduces a novel path integral formulation in terms of thermal pure states and uncovers an emergent symmetry linking entropy to Noether invariants in quantum thermodynamics.

Findings

Entropy acts as a Noether invariant during quasi-static operations.

An effective action for thermodynamic trajectories is derived.

Emergent symmetry corresponds to uniform translation of conjugate variables.

Abstract

We investigate a thermally isolated quantum many-body system with an external control represented by a time-dependent parameter. We formulate a path integral in terms of thermal pure states and derive an effective action for trajectories in a thermodynamic state space, where the entropy appears with its conjugate variable. In particular, for quasi-static operations, the symmetry for the uniform translation of the conjugate variable emerges in the path integral. This leads to the entropy as a Noether invariant.