An axiomatic definition of shannon's entropy

Nambiar, K.K.; Varma, Pramod K.; Saroch, Vandana

doi:10.1016/0893-9659(92)90084-m

Cited by 15 publications

(8 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this letter we give alternative axiomatic systems, which replace the expendability and maximality axioms with the axiom that states the uniform distribution entropy can be analytical continued if it is taken as the function of the distribution dimension, the property that has an important role in asymptotic analysis of entropy [10] (see [11] for alternative approach). The presented results generalizes discussion in [12], where the Shannon entropy is considered.…”

Section: Introductionsupporting

confidence: 83%

An axiomatic characterization of generalized entropies under analyticity condition

Ilić¹,

Stanković²

2013

Preprint

View full text Add to dashboard Cite

show abstract

Section: Introductionsupporting

confidence: 83%

An axiomatic characterization of generalized entropies under analyticity condition

Ilić¹,

Stanković²

2013

Preprint

View full text Add to dashboard Cite

show abstract

“…By our knowledge, there is no proof that (S4) and continuity are enough, but (S4) and analyticity is working. Showing the latter, in [11] an argumentation reducing everything to the rationals as above has been used.…”

Section: Further Discussionmentioning

confidence: 99%

Tsallis entropy and generalized Shannon additivity

Jäckle¹,

Keller²

2017

Preprint

View full text Add to dashboard Cite

The Tsallis entropy given for a positive parameter α can be considered as a modification of the classical Shannon entropy. For the latter, corresponding to α = 1, there exist many axiomatic characterizations. One of them based on the well-known Khinchin-Shannon axioms has been simplified several times and adapted to Tsallis entropy, where the axiom of (generalized) Shannon additivity is playing a central role. The main aim of this paper is to discuss this axiom in the context of Tsallis entropy. We show that it is sufficient for characterizing Tsallis entropy with the exceptions of cases α = 1, 2 discussed separately.

show abstract

“…where G(•) is a function of {p i }, and F (•) is another continuous function. From the axiomatic formulations of Shannon entropy [22,23,53] or nonextensive entropies [54], F and G should satisfy some axioms as (AE1) Continuity: G is continuous in ∆ d−1 and F is continuous on R;…”

Section: Appendix J: Any State Conversionmentioning

confidence: 99%

Catalytic Entropy Principles

Luo,

Wang

2021

Preprint

View full text Add to dashboard Cite

The entropy shows an unavoidable tendency of disorder in thermostatistics according to the second thermodynamics law. This provides a minimization entropy principle for quantum thermostatistics with the von Neumann entropy and nonextensive quantum thermostatistics with special Tsallis entropy. Our goal in this work is to provide operational characterizations of general entropy measures. We present the first catalytic principle consistent with the second thermodynamics law in terms of general quantum entropies for both quantum thermostatistics and nonextensive quantum thermostatistics. This further reveals new features beyond the second thermodynamics law by maximizing the cross-entropy during irreversible catalytic procedures. The present result is useful for asymptotical tasks of quantum entropy estimations and universal quantum source encoding without state tomography. It is further applied to single-shot state transitions and cooling in quantum thermodynamics with limited information. These results should be interesting in the many-body theory and long-range quantum information processing.

show abstract

An axiomatic definition of shannon's entropy

Cited by 15 publications

References 3 publications

An axiomatic characterization of generalized entropies under analyticity condition

An axiomatic characterization of generalized entropies under analyticity condition

Tsallis entropy and generalized Shannon additivity

Catalytic Entropy Principles

Contact Info

Product

Resources

About