CONVEXITY OF PARAMETER EXTENSIONS OF SOME RELATIVE OPERATOR ENTROPIES WITH A PERSPECTIVE APPROACH

AbstractIn this paper, we introduce two notions of a relative operator (α, β)-entropy and a Tsallis relative operator (α, β)-entropy as two parameter extensions of the relative operator entropy and the Tsallis relative operator entropy. We apply a perspective approach to prove the joint convexity or concavity of these new notions, under certain conditions concerning α and β. Indeed, we give the parametric extensions, but in such a manner that they remain jointly convex or jointly concave.Significance Statement. What is novel here is that we convincingly demonstrate how our techniques can be used to give simple proofs for the old and new theorems for the functions that are relevant to quantum statistics. Our proof strategy shows that the joint convexity of the perspective of some functions plays a crucial role to give simple proofs for the joint convexity (resp. concavity) of some relative operator entropies.

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On a Direct Superconducting Pairing Mechanism

Zeitschrift für Naturforschung A ◽

10.1515/zna-1999-1210 ◽

1999 ◽

Vol 54 (12) ◽

pp. 718-738 ◽

Cited By ~ 2

Author(s):

Michael C. Böhm ◽

Christoph Saal

Keyword(s):

Molecular Model ◽

Hard Core ◽

Quantum Statistics ◽

Model Systems ◽

Cooper Pairs ◽

Superconducting Transition ◽

Electron Phonon Coupling ◽

The Stability ◽

Superconducting Pairing ◽

Two Parameter

Abstract We suggest that superconductivity can be traced back to a first-order interaction between the charge carriers which does not necessarily involve second-order electron-phonon coupling. For small molecular model systems it is demonstrated that the formation of Cooper pairs can lead to an attenuation of the destabilizing influence of the Pauli antisymmetry principle (PAP). We suggest that this attenuation of a fermionic quantum constraint is the driving force for the superconducting transition. Whenever the PAP is activated in single-particle hoppings of electrons, the corresponding moves reduce the electronic derealization; they raise the ensemble energy. The stability of a fermionic system is enhanced with decreasing influence of the PAP. Moves of Cooper pairs are not influenced by any quantum constraint of the intersite type. This behaviour differs from the well-known fermionic constraints. The quantum statistics of Cooper pairs is of a mixed type combining a fermionic on-site and a bosonic intersite behaviour. It coincides with the quantum statistics of so-called hard core bosonic ensembles. In the present work Cooper pair formation has been studied for smaller molecular models. The electronic Hamiltonian employed is of the two-parameter Hubbard-type. The solid state phenomenon superconductivity is correlated with the molecular concepts of “antiaromaticity” and “aromaticity”. Arguments are given which support the present interpretation.

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A two-parameter entropy and its fundamental properties

Reviews in Mathematical Physics ◽

10.1142/s0129055x2130003x ◽

2020 ◽

pp. 2130003

Author(s):

Supriyo Dutta ◽

Shigeru Furuichi ◽

Partha Guha

Keyword(s):

Additive Property ◽

Information Theoretic ◽

Generalized Entropy ◽

Geometric Characteristics ◽

Fundamental Properties ◽

Joint Convexity ◽

Two Parameter

This article proposes a new two-parameter generalized entropy, which can be reduced to the Tsallis and Shannon entropies for specific values of its parameters. We develop a number of information-theoretic properties of this generalized entropy and divergence, for instance, the sub-additive property, strong sub-additive property, joint convexity, and information monotonicity. This article presents an exposit investigation on the information-theoretic and information-geometric characteristics of the new generalized entropy and compare them with the properties of the Tsallis and Shannon entropies.

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Some results of the Barbier-Chalonge-Divan system of stellar classification

Symposium - International Astronomical Union ◽

10.1017/s0074180900053250 ◽

1966 ◽

Vol 24 ◽

pp. 77-90 ◽

Cited By ~ 1

Author(s):

D. Chalonge

Keyword(s):

Early Type ◽

Parameter System ◽

Early Type Stars ◽

Two Parameter

Several years ago a three-parameter system of stellar classification has been proposed (1, 2), for the early-type stars (O-G): it was an improvement on the two-parameter system described by Barbier and Chalonge (3).

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Subjective Time Preference and Willingness to Pay for an Energy-Saving Durable Good

Zeitschrift für Sozialpsychologie ◽

10.1024//0044-3514.32.3.133 ◽

2001 ◽

Vol 32 (3) ◽

pp. 133-141 ◽

Cited By ~ 4

Author(s):

Gerrit Antonides ◽

Sophia R. Wunderink

Keyword(s):

Willingness To Pay ◽

Energy Saving ◽

Subjective Time ◽

Durable Good ◽

Discount Function ◽

Hyperbolic Discount ◽

The One ◽

Two Parameter ◽

Difference Effect ◽

Better Than

Summary: Different shapes of individual subjective discount functions were compared using real measures of willingness to accept future monetary outcomes in an experiment. The two-parameter hyperbolic discount function described the data better than three alternative one-parameter discount functions. However, the hyperbolic discount functions did not explain the common difference effect better than the classical discount function. Discount functions were also estimated from survey data of Dutch households who reported their willingness to postpone positive and negative amounts. Future positive amounts were discounted more than future negative amounts and smaller amounts were discounted more than larger amounts. Furthermore, younger people discounted more than older people. Finally, discount functions were used in explaining consumers' willingness to pay for an energy-saving durable good. In this case, the two-parameter discount model could not be estimated and the one-parameter models did not differ significantly in explaining the data.

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