In quantum thermodynamics, the noncommutativity of conserved quantities is a key aspect of generalized reservoirs. Squeezed-thermal reservoirs, characterized as non-Abelian thermal reservoirs with noncommuting constant quantities (charges), are redefined in this study using SU(1,1) Lie algebra generators. Our findings suggest that these reservoirs can be more accurately described as generalized Gibbs ensembles featuring three noncommuting operators instead of the generally assumed two. By incorporating three charges and the quantum phase-space method to describe dissipation into such a reservoir, two expressions for Wigner entropy production are derived: one based on the stationary mean value of the exchanged charges and another based on a single operator's stationary mean value---the Casimir operator of the Lie algebra. Analysis of these expressions across two distinct models sheds light on equilibration conditions with generalized reservoirs during the interconversion of noncommuting charges.
In quantum thermodynamics, the noncommutativity of conserved quantities is a key aspect of generalized reservoirs. Squeezed-thermal reservoirs, characterized as non-Abelian thermal reservoirs with noncommuting constant quantities (charges), are redefined in this study using SU(1,1) Lie algebra generators. Our findings suggest that these reservoirs can be more accurately described as generalized Gibbs ensembles featuring three noncommuting operators instead of the generally assumed two. By incorporating three charges and the quantum phase-space method to describe dissipation into such a reservoir, two expressions for Wigner entropy production are derived: one based on the stationary mean value of the exchanged charges and another based on a single operator's stationary mean value---the Casimir operator of the Lie algebra. Analysis of these expressions across two distinct models sheds light on equilibration conditions with generalized reservoirs during the interconversion of noncommuting charges.
We explore the perspective of considering the squeezed thermal reservoir as an equilibrium reservoir in a generalized Gibbs ensemble with two noncommuting conserved quantities. We outline the main properties of such a reservoir in terms of the exchange of energy, both heat and work, and entropy, giving some key examples to clarify its physical interpretation. This allows for a correct and insightful interpretation of all thermodynamical features of the squeezed thermal reservoir, as well as other similar nonthermal reservoirs, including the characterization of reversibility and the first and second laws of thermodynamics.
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 formulas 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 formulas. The noncommutation of charges, we find, breaks the equivalence of the formulas. Furthermore, different formulas quantify different physical effects of the noncommutation of charges 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. Published by the American Physical Society 2024
Modern quantum experiments provide examples of transport with noncommuting quantities, offering a tool to understand the interplay between thermal and quantum effects.Here we set forth a theory for non-Abelian transport in the linear response regime.Our key insight is to use generalized Gibbs ensembles with noncommuting charges as the basic building blocks and strict charge-preserving unitaries in a collisional setup.The linear response framework is then built using a collisional model between two reservoirs.We show that the transport coefficients obey Onsager reciprocity.Moreover, we find that quantum coherence, associated with the noncommutativity, acts so as to reduce the net entropy production, when compared to the case of commuting transport.This therefore provides a clear connection between quantum coherent transport and dissipation.As an example, we study heat and squeezing fluxes in bosonic systems, characterizing a set of thermosqueezing coefficients with potential applications in metrology and heat-to-work conversion in the quantum regime.
In statistical mechanics, a small system exchanges conserved quantities-heat, particles, electric charge, etc.-with a bath. The small system thermalizes to the canonical ensemble or the grand canonical ensemble, etc., depending on the quantities. The conserved quantities are represented by operators usually assumed to commute with each other. This assumption was removed within quantum-information-theoretic (QI-theoretic) thermodynamics recently. The small system's long-time state was dubbed "the non-Abelian thermal state (NATS)." We propose an experimental protocol for observing a system thermalize to the NATS. We illustrate with a chain of spins, a subset of which forms the system of interest. The conserved quantities manifest as spin components. Heisenberg interactions push the conserved quantities between the system and the effective bath, the rest of the chain. We predict long-time expectation values, extending the NATS theory from abstract idealization to finite systems that thermalize with finite couplings for finite times. Numerical simulations support the analytics: The system thermalizes to near the NATS, rather than to the canonical prediction. Our proposal can be implemented with ultracold atoms, nitrogen-vacancy centers, trapped ions, quantum dots, and perhaps nuclear magnetic resonance. This work introduces noncommuting conserved quantities from QI-theoretic thermodynamics into quantum many-body physics: atomic, molecular, and optical physics and condensed matter.
We consider a many-body Hilbert space with a fixed global charge and show that the typical entanglement entropy of a subsystem, at the leading and subleading order in the thermodynamic limit, can be expressed in terms of a single quantity which represents the local thermal entropy at fixed charge density. We find a general formula which applies both to abelian U(1) symmetry and non-abelian SU(2) symmetry, including the case of a local Hilbert space which transforms under a general reducible representation of the symmetry group. We illustrate the general formula with model systems and discuss the relevance of the results as a probe of quantum chaos for physical Hamiltonians.
Quantum simulators have recently enabled experimental observations of the internal thermalization of quantum many-body systems.Often, the global energy and particle number are conserved and the system is prepared with a well-defined particle number-in a microcanonical subspace.However, quantum evolution can also conserve quantities, or charges, that fail to commute with each other.Noncommuting charges have recently emerged as a subfield at the intersection of quantum thermodynamics and quantum information.Until now, this subfield has remained theoretical.We initiate the experimental testing of its predictions, with a trapped-ion simulator.We prepare 6-21 spins in an approximate microcanonical subspace, a generalization of the microcanonical subspace for accommodating noncommuting charges, which cannot necessarily have well-defined nontrivial values simultaneously.We simulate a Heisenberg evolution using laser-induced entangling interactions and collective spin rotations.The noncommuting charges are the three spin components.We find that small subsystems equilibrate to near a recently predicted non-Abelian thermal state.This work bridges quantum many-body simulators to the quantum thermodynamics of noncommuting charges, the predictions of which can now be tested.