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Non-Abelian transport distinguishes three usually equivalent notions of entropy production (2305.15480v2)

Published 24 May 2023 in quant-ph, cond-mat.stat-mech, and physics.chem-ph

Abstract: We extend entropy production to a deeply quantum regime involving noncommuting conserved quantities. Consider a unitary transporting conserved quantities ("charges") between two systems initialized in thermal states. Three common formulae model the entropy produced. They respectively cast entropy as an extensive thermodynamic variable, as an information-theoretic uncertainty measure, and as a quantifier of irreversibility. Often, the charges are assumed to commute with each other (e.g., energy and particle number). Yet quantum charges can fail to commute. Noncommutation invites generalizations, which we posit and justify, of the three formulae. Charges' noncommutation, we find, breaks the formulae's equivalence. Furthermore, different formulae quantify different physical effects of charges' noncommutation on entropy production. For instance, entropy production can signal contextuality - true nonclassicality - by becoming nonreal. This work opens up stochastic thermodynamics to noncommuting - and so particularly quantum - charges.

Citations (11)

Summary

  • The paper demonstrates that noncommuting charges break the usual equivalence among thermodynamic, information-theoretic, and irreversibility-based entropy definitions.
  • It employs numerical simulations with two qubits to show how quantum coherence and contextuality reduce average entropy production.
  • The findings imply that quantum thermodynamic models and engine designs must adapt to account for nonclassical entropy behavior.

Overview of Entropy Production with Noncommuting Charges

The paper focuses on extending the concept of entropy production to quantum systems governed by noncommuting conserved quantities. The paper originates from the need to understand entropy in a regime where standard thermodynamic intuitions about commuting quantities, like energy and particle number, do not apply. The researchers explore three common approaches for constructing entropy production formulae, usually assumed to coincide: a thermodynamic variable, an information-theoretic uncertainty measure, and an indicator of irreversibility. Their research specifically targets the influence of noncommuting charges, exploring how these influence the divergence of the aforementioned definitions and pave the way for a nuanced understanding of entropy.

Noncommuting Charges and Quantum Contextuality

A core contribution of the paper is its treatment of entropy production under conditions where noncommuting charges disrupt the usual equivalence between different formulae. The authors elucidate the physical scenarios leading to this divergence. Notably, they identify how noncommuting charges invite phenomena such as the emergence of nonreal quasiprobabilities, which could signify nonclassicality or quantum contextuality. This nonclassicality contrasts with the classical, commuting scenarios traditionally studied in thermodynamics and stands out through nonreal SEP, highlighting the contextual nature of quantum measurements and dynamics.

Numerical Results and Practical Implications

The numerical simulations involving two qubits exchanging noncommuting charges strongly support the theoretical advancements proposed. The examination of entropy production within such systems reveals significant insights, particularly the relation between coherence, quantum contextuality, and the reduction of average entropy production—a reflection on how quantum systems might operate differently from classical predictions.

The implications are multifold, suggesting that thermodynamic models of quantum information processing systems must consider these newly revealed quantum aspects. More importantly, these findings can influence the design of quantum engines and algorithms that exploit quantum coherence to achieve efficiency gains unattainable by classical analogs.

Theoretical and Practical Considerations

On the theoretical front, this work positions itself within the discourse on the second law's generalization to quantum contexts, insisting it splits into multiple "laws" for noncommuting systems. Future research should explore the manifold ways such entropy formulations impact quantum thermodynamic uncertainty relations, quantum feedback, and control. Practically, implementing the findings could necessitate advanced experimental techniques for weak measurements and the control of noncommuting quantum observables.

Conclusion

In conclusion, this paper provides pivotal insights into a less explored and physically complex area of quantum thermodynamics. By scrutinizing the distinctions brought about by noncommuting charges, the paper does not only challenge standard entropy conceptions but establishes a foundation for potentially revolutionary developments in quantum technologies. The work inspires both theoretical and experimental explorations into the dynamics of complex quantum systems ruled by noncommuting algebraic structures.

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