Third Law of Thermodynamics as a Single Inequality

Abstract

The third law of thermodynamics in the form of the unattainability principle states that exact ground-state cooling requires infinite resources. Here we investigate the amount of non-equilibrium resources needed for approximate cooling. We consider as resource any system out of equilibrium, allowing for resources beyond the i.i.d. assumption and including the input of work as a particular case. We establish in full generality a sufficient and a necessary condition for cooling and show that for a vast class of non-equilibrium resources these two conditions coincide, providing a single necessary and sufficient criterion. Such conditions are expressed in terms of a single function playing a similar role for the third law to the one of the free energy for the second law. From a technical point of view we provide new results about concavity/convexity of certain Renyi-divergences, which might be of independent interest.

Extended discussion on approximated and exact catalysts and models for the source of work. 22 pages. 2 Figures

References in corpus (10)

• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Quantum coherence, time-translation symmetry and thermodynamics
• The thermodynamic meaning of negative entropy
• Autonomous Quantum Refrigerator in a Circuit-QED Architecture Based on a Josephson Junction
• Gibbs-Preserving Maps outperform Thermal Operations in the quantum regime
• Quantum bath refrigeration towards absolute zero: unattainability principle challenged
• Quantum Relative Lorenz Curves
• Fundamental limits for cooling of linear quantum refrigerators
• Quantum resources for purification and cooling: fundamental limits and opportunities
• The Asymptotic Cooling of Heat-Bath Algorithmic Cooling

Cited by in corpus (44)

• An introductory review of the resource theory approach to thermodynamics
• Ideal Projective Measurements Have Infinite Resource Costs
• Landauer vs. Nernst: What is the True Cost of Cooling a Quantum System?
• Correlating thermal machines and the second law at the nanoscale
• MBL-mobile: Quantum engine based on many-body localization
• Von Neumann entropy from unitarity
• Fundamental limits on low-temperature quantum thermometry with finite resolution
• Unifying paradigms of quantum refrigeration: A universal and attainable bound on cooling
• Work estimation and work fluctuations in the presence of non-ideal measurements
• Quantum field thermal machines
• Correlation in Catalysts Enables Arbitrary Manipulation of Quantum Coherence
• Smoothed generalized free energies for thermodynamics
• Operational definition of the temperature of a quantum state
• Unifying paradigms of quantum refrigeration: fundamental limits of cooling and associated work costs
• Not quite free shortcuts to adiabaticity
• Energy-Consumption Advantage of Quantum Computation
• Continuous thermomajorization and a complete set of laws for Markovian thermal processes
• Exponential improvement for quantum cooling through finite-memory effects
• Optimizing thermalizations
• Fundamental limits on anomalous energy flows in correlated quantum systems
• Autonomous Quantum Devices: When Are They Realizable without Additional Thermodynamic Costs?
• Quantum measurements constrained by the third law of thermodynamics
• Thermodynamically optimal creation of correlations
• How much can we cool a quantum oscillator? A useful analogy to understand laser cooling as a thermodynamical process
• Catalysis in Action via Elementary Thermal Operations
• Entanglement generation in quantum thermal machines
• A hierarchy of thermal processes collapses under catalysis
• Quantum catalysis in cavity quantum electrodynamics
• Catalytic transformations for thermal operations
• Cooling to absolute zero: The unattainability principle
• Thermodynamic optimization of quantum algorithms: On-the-go erasure of qubit registers
• Quantum Coding with Finite Thermodynamic Resources
• Catalytic transformations with finite-size environments: applications to cooling and thermometry
• Photon cooling: linear vs nonlinear interactions
• Thermodynamic state convertibility is determined by qubit cooling and heating
• Thermalization of finite complexity and its application to heat bath algorithmic cooling
• Cooling a Qubit using n Others
• Unlocking inaccessible performance of the quantum refrigerator with catalysts
• Minimizing Dissipation via Interacting Environments: Quadratic Convergence to Landauer Bound
• Catalytic Activation of Bell Nonlocality
• Cooling and work extraction under memory-assisted Markovian thermal processes
• Finite-size catalysis in quantum resource theories
• Thermodynamic Constraints on Information Transmission in Quantum Ensembles
• Time-cost-error trade-off relation in thermodynamics: The third law and beyond