Maximum Entropy Principle in statistical inference: case for non-Shannonian entropies

Abstract

In this letter we show that the Shore--Johnson axioms for Maximum Entropy Principle in statistical estimation theory account for a considerably wider class of entropic functional than previously thought. Apart from a formal side of the proof, we substantiate our point by analyzing the effect of weak correlations and discuss two pertinent examples: $2$-qubit quantum system and strongly interacting nuclear systems.

to appear in Phys. Rev. Lett., 6 pages, 6 pages of Supplementary material

References in corpus (12)

• Zeroth Law compatibility of non-additive thermodynamics
• Multiplicity fluctuations due to the temperature fluctuations in high-energy nuclear collisions
• Generalized non-additive entropies and quantum entanglement
• Systematic Analysis of the Non-extensive Statistical Approach in High Energy Particle Collisions - Experiment vs. Theory
• Towards a relativistic statistical theory
• Unidirectional Random Growth with Resetting
• Generalized statistics: yet another generalization
• Classification of complex systems by their sample-space scaling exponents
• Tsallis thermostatics as a statistical physics of random chains
• Conceptual Inadequacy of the Shore and Johnson Axioms for Wide Classes of Complex Systems
• The world according to Renyi: Thermodynamics of multifractal systems
• Entropies for complex systems: generalized-generalized entropies

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