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Unification of observational entropy with maximum entropy principles
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We introduce a definition of coarse-grained entropy that unifies measurement-based (observational entropy) and max-entropy-based (Jaynes) approaches to coarse-graining, by identifying physical constraints with information theoretic priors. The definition is shown to include as special cases most other entropies of interest in physics. We then consider second laws, showing that the definition admits new entropy increase theorems and connections to thermodynamics. We survey mathematical properties of the definition, and show it resolves some pathologies of the traditional observational entropy in infinite dimensions. Finally, we study the dynamics of this entropy in a quantum random matrix model and a classical hard sphere gas. Together the results suggest that this generalized observational entropy can form the basis of a highly general approach to statistical mechanics.
Forward citations
Cited by 3 Pith papers
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Work and entropy of mixing in isolated quantum systems
Mixing entropy is identified with observational entropy, yielding a Landauer-like work-difference bound with an observational temperature, and a resolution of the Gibbs mixing paradox in isolated quantum systems.
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Coarse-grained quantum thermodynamics: Observation-dependent quantities, observation-independent laws
A framework for coarse-grained quantum thermodynamics in which resolution-dependent, temperature-dependent energy levels are defined so that second-law inequalities and work fluctuation theorems remain valid at any me...
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Maximum entropy principle for quantum processes
The paper's central theorem, that energy-constrained quantum channels maximize channel entropy if and only if they are absolutely thermalizing, is false: other channels can also reach the maximum.
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