Thermodynamic limits of dynamic cooling

Abstract

We study dynamic cooling, where an externally driven two-level system is cooled via reservoir, a quantum system with initial canonical equilibrium state. We obtain explicitly the minimal possible temperature $T_{\min }>0$ reachable for the two-level system. The minimization goes over all unitary dynamic processes operating on the system and reservoir, and over the reservoir energy spectrum. The minimal work needed to reach $T_{\min }$ grows as $1/T_{\min }$. This work cost can be significantly reduced, though, if one is satisfied by temperatures slightly above $T_{\min }$. Our results on $T_{\min }>0$ prove unattainability of the absolute zero temperature without ambiguities that surround its derivation from the entropic version of the third law. The unattainability can be recovered, albeit via a different mechanism, for cooling by a reservoir with an initially microcanonic state. We also study cooling via a reservoir consisting of $N\gg 1$ identical spins. Here we show that $T_{\min }\propto \frac{1}{N}$ and find the maximal cooling compatible with the minimal work determined by the free energy.

18 pages, 4 figures; submitted to PRE

References in corpus (11)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Ground state lost but degeneracy found: the effective thermodynamics of artificial spin ice
• Optimal refrigerator
• The Quantum Refrigerator: The quest for absolute zero
• Thermodynamic versus statistical nonequivalence of ensembles for the mean-field Blume-Emery-Griffiths model
• Stochastic pumping of heat: Approaching the Carnot efficiency
• Gedanken experiments on nearly extremal black holes and the Third Law
• On the Casimir entropy for a ball in front of a plane
• A Cyclic Cooling Algorithm
• On the mean-field spherical model
• Work extraction from microcanonical bath

Cited by in corpus (45)

• An improved Landauer Principle with finite-size corrections
• A derivation (and quantification) of the third law of thermodynamics
• Ideal Projective Measurements Have Infinite Resource Costs
• Landauer vs. Nernst: What is the True Cost of Cooling a Quantum System?
• Performance of autonomous quantum thermal machines: Hilbert space dimension as a thermodynamic resource
• Unifying paradigms of quantum refrigeration: A universal and attainable bound on cooling
• Fundamental limits for cooling of linear quantum refrigerators
• Third Law of Thermodynamics as a Single Inequality
• Quantum resources for purification and cooling: fundamental limits and opportunities
• Short Time Cycles of Purely Quantum Refrigerators
• The Asymptotic Cooling of Heat-Bath Algorithmic Cooling
• Ground state cooling is not possible given initial system-thermal bath factorization
• Quantum Horn's lemma, finite heat baths, and the third law of thermodynamics
• A quantum Otto engine with finite heat baths: energy, correlations, and degradation
• Quantum effects improve the energy efficiency of feedback control
• Task-dependent control of open quantum systems
• Efficiency of a cyclic quantum heat engine with finite-size baths
• Conditional work statistics of quantum measurements
• Novel Technique for Robust Optimal Algorithmic Cooling
• Minimising the heat dissipation of quantum information erasure
• Dynamic Cooling on Contemporary Quantum Computers
• Low-control and robust quantum refrigerator and applications with electronic spins in diamond
• Quantum measurements constrained by the third law of thermodynamics
• Two constructive proofs on d-majorization and thermo-majorization
• How much can we cool a quantum oscillator? A useful analogy to understand laser cooling as a thermodynamical process
• Designing refrigerators in higher dimensions using quantum spin models
• Entanglement generation in quantum thermal machines
• The interplay between cycle geometry and performance of sudden refrigerators
• No-go Theorem of Purification
• Electromagnetic gauge-freedom and work
• Free energy for non-equilibrium quasi-stationary states
• Generalized Zurek's bound on the cost of an individual classical or quantum computation
• Cooling to absolute zero: The unattainability principle
• The EPR Paradox Implies A Minimum Achievable Temperature
• Fast, Accurate, and Local Temperature Control Using Qubits
• Photon cooling: linear vs nonlinear interactions
• Catalytic transformations with finite-size environments: applications to cooling and thermometry
• Defining work done on electromagnetic field
• Does universal controllability of physical systems prohibit thermodynamic cycles?
• Fundamental precision limits in finite-dimensional quantum thermal machines
• Cooling a Qubit using n Others
• Unlocking inaccessible performance of the quantum refrigerator with catalysts
• Optimal Manipulation Of Correlations And Temperature In Quantum Thermodynamics
• Cooling and work extraction under memory-assisted Markovian thermal processes
• Time-cost-error trade-off relation in thermodynamics: The third law and beyond