Unifying Aspects of Generalized Calculus

Abstract

Non-Newtonian calculus naturally unifies various ideas that have occurred over the years in the field of generalized thermostatistics, or in the borderland between classical and quantum information theory. The formalism, being very general, is as simple as the calculus we know from undergraduate courses of mathematics. Its theoretical potential is huge, and yet it remains unknown or unappreciated.

Submitted to Entropy, special issue on statistical aspects of entropy

References in corpus (4)

• A possible deformed algebra and calculus inspired in nonextensive thermostatistics
• Towards a relativistic statistical theory
• Arithmetic loophole in Bell's theorem: An overlooked threat to entangled-state quantum cryptography
• On the extended Kolmogorov-Nagumo information-entropy theory, the q -> 1/q duality and its possible implications for a non-extensive two dimensional Ising model

Cited by in corpus (6)

• On a Non-Newtonian Calculus of Variations
• Thermodynamics of exponential Kolmogorov-Nagumo averages
• Imitating quantum probabilities: Beyond Bell's theorem and Tsirelson bounds
• Along the lines of nonadditive entropies: $q$-prime numbers and $q$-zeta functions
• On the Relativity of Quantumness as Implied by Relativity of Arithmetic and Probability
• A Non-Newtonian Noether's Symmetry Theorem