Geometric Curvature Governs Work in Open Quantum Steady States

TL;DR

This paper demonstrates that in open quantum steady states, work is governed by an emergent geometric curvature in control space, linking coherence and thermodynamic response.

Contribution

It introduces a geometric framework for open quantum thermodynamics, showing curvature determines work in driven dissipative quantum systems.

Findings

Work in quantum steady states is linked to a geometric curvature in control space.

Coherence is necessary for nontrivial geometric effects in work.

Reversing cycle orientation changes the sign of work, confirming geometric origin.

Abstract

Classical thermodynamics admits a geometric formulation in which work is associated with areas enclosed by cycles in state space. Whether an analogous structure persists in driven, dissipative quantum systems remains an open question. Here we show that quasistatic work in open quantum steady states is governed by an emergent geometric curvature in control-parameter space arising from steady-state coherence. For a driven dissipative two-level system, we construct a work one-form whose curvature determines the work produced in cyclic processes. The work vanishes under strong dephasing, identifying coherence as a necessary condition for nontrivial geometry. However, its magnitude is set not by the coherence itself but by the spatial structure of the curvature: cycles enclosing comparable areas produce different work depending on their location in parameter space. Reversing the cycle orientation reverses the sign of the work, confirming its geometric origin. These results establish a geometric framework for open quantum thermodynamics and identify curvature as the organizing principle of thermodynamic response, with direct implications for driven light--matter systems in cavity quantum electrodynamics.