Operational definition of the temperature of a quantum state
arXiv:2205.00017 · doi:10.1103/PhysRevLett.130.040401
Abstract
Temperature is usually defined for physical systems at thermal equilibrium. Nevertheless one may wonder if it would be possible to attribute a meaningful notion of temperature to an arbitrary quantum state, beyond simply the thermal (Gibbs) state. In this work, we propose such a notion of temperature considering an operational task, inspired by the Zeroth Law of thermodynamics. Specifically, we define two effective temperatures for quantifying the ability of a quantum system to cool down or heat up a thermal environment. In this way we can associate an operationally meaningful notion of temperature to any quantum density matrix. We provide general expressions for these effective temperatures, for both single- and many-copy systems, establishing connections to concepts previously discussed in the literature. Finally, we consider a more sophisticated scenario where the heat exchange between the system and the thermal environment is assisted by a quantum reference frame. This leads to an effect of "coherent quantum catalysis", where the use of a coherent catalyst allows for exploiting quantum energetic coherences in the system, now leading to much colder or hotter effective temperatures.
arXiv comment4+9 pages. Close to published version
References in corpus (63)
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- Nonequilibrium dynamics of closed interacting quantum systems
- Many body localization and thermalization in quantum statistical mechanics
- The large deviation approach to statistical mechanics
- Many-body localization, thermalization, and entanglement
- Quantum many-body systems out of equilibrium
- Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
- Quantum Thermodynamic Cycles and quantum heat engines
- Fundamental limitations for quantum and nano thermodynamics
- Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
- The second laws of quantum thermodynamics
- Extractable work from ensembles of quantum batteries. Entanglement helps
- A nano heat engine beyond the Carnot limit
- The Physics and Mathematics of the Second Law of Thermodynamics
- Catalytic Coherence
- Quantum coherence, time-translation symmetry and thermodynamics
- Entanglement-assisted local manipulation of pure quantum states
- The extraction of work from quantum coherence
- Towards fully quantum second laws of thermodynamics: limitations on the evolution of quantum coherences
- Quantum-enhanced absorption refrigerators
- Virtual qubits, virtual temperatures, and the foundations of thermodynamics
- An introductory review of the resource theory approach to thermodynamics
- Temperature in and out of equilibrium: a review of concepts, tools and attempts
- Quantum thermal absorption machines: refrigerators, engines and clocks
- Efficiency of heat engines coupled to nonequilibrium reservoirs
- Reversing the direction of heat flow using quantum correlations
- Locality of temperature
- Entanglement and the Thermodynamic Arrow of Time
- Eigenstate Thermalization in a Locally Perturbed Integrable System
- Existence of temperature on the nanoscale
- Thermalization and canonical typicality in translation-invariant quantum lattice systems
- Correlating thermal machines and the second law at the nanoscale
- A short note on passivity, complete passivity and virtual temperatures
- Von Neumann entropy from unitarity
- Performance of autonomous quantum thermal machines: Hilbert space dimension as a thermodynamic resource
- Limits to catalysis in quantum thermodynamics
- Catalytic quantum teleportation and beyond
- Thermodynamic work from operational principles
- Quantum thermodynamics of correlated-catalytic state conversion at small-scale
- Construction of microcanonical entropy on thermodynamic pillars
- Coherence and asymmetry cannot be broadcast
- Role of quantum coherence in the thermodynamics of energy transfer
- A no-broadcasting theorem for quantum asymmetry and coherence and a trade-off relation for approximate broadcasting
- Third Law of Thermodynamics as a Single Inequality
- Beyond the thermodynamic limit: finite-size corrections to state interconversion rates
- Meaning of temperature in different thermostatistical ensembles
- Entropy and reversible catalysis
- The ontology of temperature in nonequilibrium systems
- All states are universal catalysts in quantum thermodynamics
- Taking the temperature of a pure quantum state
- Intensive temperature and quantum correlations for refined quantum measurements
- Is coherence catalytic?
- Locality of temperature in spin chains
- Optimizing thermalizations
- By-passing fluctuation theorems
- Nonequilibrium Quantum Free Energy and Effective Temperature, Generating Functional and Influence Action
- Extracting work from correlated many-body quantum systems
- The geometry of passivity for quantum systems and a novel elementary derivation of the Gibbs state
- Molecular dynamics investigations on a quantum system in a thermostat
- Energy upper bound for structurally stable N-passive states
- Locality of temperature and correlations in the presence of non-zero-temperature phase transitions
- Thermodynamic laws in isolated systems
Cited by in corpus (20)
- Catalysis of entanglement and other quantum resources
- Fundamental limits on anomalous energy flows in correlated quantum systems
- Heat as a witness of quantum properties
- Covariant catalysis requires correlations and good quantum reference frames degrade little
- Correlated quantum machines beyond the standard second law
- Experimentally probing Landauer's principle in the quantum many-body regime
- Complete Characterization of Entanglement Embezzlement
- Quantum catalysis in cavity quantum electrodynamics
- Catalytic transformations for thermal operations
- Dynamical Landauer principle: Thermodynamic criteria of transmitting classical information
- Spectral Bounds on Entropy and Ergotropy via Statistical Effective Temperature in Classical Polarization and Quantum Thermal States
- Teleportation with Embezzling Catalysts
- Topological quantum thermometry
- Resolving the Debate Between Boltzmann and Gibbs Entropy: Relative Energy Window Eliminates Thermodynamic Inconsistencies and Allows Negative Absolute Temperatures
- Communication with Quantum Catalysts
- Thermodynamic state convertibility is determined by qubit cooling and heating
- Minimizing Dissipation via Interacting Environments: Quadratic Convergence to Landauer Bound
- Direct temperature readout in nonequilibrium quantum thermometry
- Finite-size catalysis in quantum resource theories
- Time-cost-error trade-off relation in thermodynamics: The third law and beyond