Convergence of macrostates under reproducible processes

Abstract

I show that whenever a system undergoes a reproducible macroscopic process the mutual distinguishability of macrostates, as measured by their relative entropy, diminishes. This extends the second law which regards only ordinary entropies, and hence only the distinguishability between macrostates and one specific reference state (equidistribution). The new result holds regardless of whether the process is linear or nonlinear. Its proof hinges on the monotonicity of quantum relative entropy under arbitrary coarse grainings, even those that cannot be represented by completely positive maps.

5 pages, no figures; v2: new title and abstract, expanded on motivation and physical meaning

References in corpus (4)

• The Role of Relative Entropy in Quantum Information Theory
• Entanglement Theory and the Second Law of Thermodynamics
• From Reversible Quantum Microdynamics to Irreversible Quantum Transport
• A Generalization of Quantum Stein's Lemma

Cited by in corpus (7)

• Quantifying non-Gaussianity for quantum information
• Resource theory of non-Gaussian operations
• Quantifying non-Gaussianity of quantum-state correlation
• Comment on "Convergence of macrostates under reproducible processes" [Phys. Lett. A 374: 3715-3717 (2010)]
• Unifying Treatment of Discord via Relative Entropy
• Assessing thermalization and estimating the Hamiltonian with output data only
• Quantum marginal inequalities and the conjectured entropic inequalities