The thermodynamic meaning of negative entropy

Abstract

Landauer's erasure principle exposes an intrinsic relation between thermodynamics and information theory: the erasure of information stored in a system, S, requires an amount of work proportional to the entropy of that system. This entropy, H(S|O), depends on the information that a given observer, O, has about S, and the work necessary to erase a system may therefore vary for different observers. Here, we consider a general setting where the information held by the observer may be quantum-mechanical, and show that an amount of work proportional to H(S|O) is still sufficient to erase S. Since the entropy H(S|O) can now become negative, erasing a system can result in a net gain of work (and a corresponding cooling of the environment).

Added clarification on non-cyclic erasure and reversible computation (Appendix E). For a new version of all technical proofs see the Supplementary Information of the journal version (free access)

References in corpus (26)

• Separability of Mixed States: Necessary and Sufficient Conditions
• Introducing Quantum Discord
• Strengths and Weaknesses of Quantum Computing
• Black holes as mirrors: quantum information in random subsystems
• The Uncertainty Principle in the Presence of Quantum Memory
• Unified View of Quantum and Classical Correlations
• The operational meaning of min- and max-entropy
• The Physics of Maxwell's demon and information
• A Thermodynamical Approach to Quantifying Quantum Correlations
• Quantum information can be negative
• Local versus non-local information in quantum information theory: formalism and phenomena
• The thermodynamic meaning of negative entropy
• Interpreting quantum discord through quantum state merging
• Operational interpretations of quantum discord
• Quantum Discord and Maxwell's Demons
• Symmetry implies independence
• A Fully Quantum Asymptotic Equipartition Property
• Duality Between Smooth Min- and Max-Entropies
• Einselection and Decoherence from an Information Theory Perspective
• The physics of forgetting: Landauer's erasure principle and information theory
• The work value of information
• Entanglement and the Thermodynamic Arrow of Time
• Entanglement irreversibility from quantum discord and quantum deficit
• Generalising Landauer's Principle
• The decoupling approach to quantum information theory
• The thermodynamic cost of reliability and low temperatures: Tightening Landauer's principle and the Second Law

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