Berry-Phase-Induced Chirality in Thermodynamics

Abstract: Geometric phases are foundational to isolated quantum systems, yet their thermodynamic role in open systems remains unrevealed Developing a dissipative adiabatic perturbation expansion, we discover a Berry-phase-induced chiral work difference that survives decoherence. This chirality evolves from an interferometric thermodynamic Aharonov-Bohm effect in the unitary regime to a fringe-free signal in the dissipative regime. We illustrate this framework in a two-level system and assess its experimental feasibility. Our findings clarify the role of quantum geometry in the geometric formulation of thermodynamics.

• The paper presents the DAPE framework, which separates dissipative work into symmetric metric and chiral Berry-phase contributions in open quantum systems.
• It demonstrates that Berry-phase-induced chirality persists as a measurable thermodynamic signal even under strong decoherence, challenging conventional intuition.
• Analytical and numerical results on a two-level system show the chiral work difference scales as O(1/T²), making it experimentally accessible via platforms like NMR.

Berry Phase-Induced Chirality in Open Quantum Thermodynamics

Geometric Phases and Thermodynamic Chirality

The paper "Berry-Phase-Induced Chirality in Thermodynamics" (2605.13685) addresses the reincorporation of geometric phases, specifically the Berry phase, into the thermodynamics of open quantum systems—a domain where decoherence classically suppresses quantum interference effects. The authors introduce the Dissipative Adiabatic Perturbation Expansion (DAPE) for analyzing open quantum systems subjected to slow, periodic driving, focusing on how Berry phase effects persist and imprint chirality in dissipated work even under strong decoherence.

Geometric phases are foundational in quantum theory, manifesting in adiabatic evolution as the Berry phase: a gauge-invariant phase tied to the curvature of the parameter manifold. While traditionally a hallmark of unitary, isolated quantum systems, its signature in open, dissipative systems has been elusive, owing to decoherence degrading coherent geometric signals.

DAPE Framework: Thermodynamic Chirality from Berry Phase

The core innovation is the DAPE approach, which systematically expands the master equation for driven open systems and separates first-order dissipative work, governed by the thermodynamic metric (Riemannian), from second-order Berry-phase-induced contributions. The average work is decomposed into a symmetric (metric) term and a chiral (Berry-phase) term. The Berry-phase-induced term is isolated by considering reversible driving protocols (clockwise vs. counterclockwise), thereby revealing a chiral work difference $\Delta W$—the macroscopic manifestation of quantum geometric chirality.

In the unitary regime, $\Delta W$ oscillates with the driving period, embodying an interferometric "thermodynamic Aharonov-Bohm effect," where the extra dissipated work encodes interference between dynamical and geometric phase channels. This constitutes a non-equilibrium thermodynamic observable directly sensitive to quantum geometric structure.

In the dissipative regime, with strong dephasing ($\gamma_{mn} \gg T^{-1}$), these oscillations are washed out, but the chiral work difference persists and becomes a fringe-free thermodynamic signal, allowing direct readout of the Berry phase from irreversible dissipation. Contrary to established intuition, the Berry phase does not vanish in the classical limit; rather, it imprints a robust signature into chiral, irreversible thermodynamic quantities.

Two-Level System Application and Analytical Results

The paper applies the framework to a two-level system driven by a precessing magnetic field. The Hamiltonian is $$-\frac{\hbar \omega}{2} \mathbf{n}(t) \cdot \hat{\boldsymbol{\sigma}}$$, with $\mathbf{n}(t)$ parametrized by polar and azimuthal angles. The Berry phase is proportional to the solid angle traced on the Bloch sphere. Analytical expressions for both symmetric and chiral components of dissipation are obtained; the geometric metric yields a thermodynamic length $\mathcal{L}$, bounding the leading-order work dissipation via $\hbar\mathcal{L}^2/T$, and the Berry phase difference $\Phi$ controls the $\mathcal{O}(T^{-2})$ chiral work contribution.

Strong numerical results include:

• Chiral work difference scaling: $\Delta W$ persists as $\Delta W$0 across both unitary and dissipative regimes, while symmetric dissipation crosses over from $\Delta W$1 to $\Delta W$2 scaling.
• Explicit two-level system calculations: For typical NMR parameters, single-spin chiral work signals in the unitary regime are experimentally accessible, and macroscopic ensembles amplify the dissipative regime signals to resolvable levels.
• Rigorous analytical validation: Exact solutions of Bloch equations corroborate the DAPE predictions.

The analytic structure identifies special symmetry cases (e.g., $\Delta W$3), where chirality vanishes, and parameter regimes where it is maximized.

Theoretical and Practical Implications

This study demonstrates a direct geometric encoding of quantum coherence via irreversible thermodynamic quantities, extending the geometric paradigm of thermodynamics to include Berry-phase-induced chirality. Importantly, this overturns the intuition that classical dissipation erases all quantum geometric imprints; instead, the Berry phase survives as a chiral dissipative correction that is robust to decoherence.

From an experimental standpoint, the results indicate feasibility for measurement in platforms such as NMR, spin ensembles, and superconducting circuits, especially for systems with intrinsic collective amplification. The connection between geometric phase and chiral dissipation opens pathways for probing quantum geometry in strongly interacting or many-body settings, potentially amplifying these effects to macroscopic observables.

Outlook

The DAPE expansion constitutes a systematic tool for quantifying geometric phase effects in open quantum thermodynamics beyond the two-level paradigm, including many-body and strongly collective systems. Future development can harness collective quantum coherence to enhance chiral signals, providing a thermodynamic probe for quantum geometric structure in complex environments. Moreover, the identification of robust thermodynamic chirality has implications for the optimization and control of quantum thermal machines, quantum information protocols, and non-equilibrium statistical mechanics, potentially informing geometric principles for minimizing dissipation in driven quantum devices.

Conclusion

The paper rigorously establishes that Berry-phase-induced chirality survives the quantum-to-classical crossover in open driven systems, imprinting a measurable chiral work difference in thermodynamic observables. The DAPE framework delineates geometric and chiral contributions, validating analytical predictions with exact solutions. This work elucidates the geometric origins of irreversible thermodynamics and sets the stage for probing quantum geometry via dissipation in diverse quantum platforms.