205 citations · 3.3k across the 120 of their papers we have counts for
9 papers · 2 filters
Nonextensive thermodynamic relations
Sumiyoshi Abe, S. Martinez, F. Pennini +1
The generalized zeroth law of thermodynamics indicates that the physical temperature in nonextensive statistical mechanics is different from the inverse of the Lagrange multiplier,…
Macroscopic thermodynamics of equilibrium characterized by power-law canonical distributions
Sumiyoshi Abe, A. K. Rajagopal
Macroscopic thermodynamics of equilibrium is constructed for systems obeying power-law canonical distributions. With this, the connection between macroscopic thermodynamics and mic…
Rates of convergence of nonextensive statistical distributions to Levy distributions in full and half spaces
Sumiyoshi Abe, A. K. Rajagopal
The Levy-type distributions are derived using the principle of maximum Tsallis nonextensive entropy both in the full and half spaces. The rates of convergence to the exact Levy sta…
Ideal gas in nonextensive optimal Lagrange multipliers formalism
Sumiyoshi Abe, S. Martinez, F. Pennini +1
Based on the prescription termed the optimal Lagrange multipliers formalism for extremizing the Tsallis entropy indexed by q, it is shown that key aspects of the treatment of the i…
A problem with the escort distribution representation of nonextensive statistical mechanics
Sumiyoshi Abe
It is pointed out that the Tsallis entropy functional represented in terms of the escort distribution is not concave of the entropic index is less than unity. It is emphasized…
Axioms and uniqueness theorem for Tsallis entropy
Sumiyoshi Abe
The Shannon-Khinchin axioms for the ordinary information entropy are generalized in a natural way to the nonextensive systems based on the concept of nonextensive conditional entro…
Justification of Power-Law Canonical Distributions Based on Generalized Central Limit Theorem
Sumiyoshi Abe, A. K. Rajagopal
A self-consistent thermodynamic framework is presented for power-law canonical distributions based on the generalized central limit theorem by extending the discussion given by Khi…
Properties of convergence of nonextensive statistical distribution to the Levy distribution
Sumiyoshi Abe, A. K. Rajagopal
It is shown that the distribution derived from the principle of maximum Tsallis entropy is a superposable Levy-type distribution. Concomitantly, the leading order correction to the…
Microcanonical Foundation for Systems with Power-Law Distributions
Sumiyoshi Abe, and A. K. Rajagopal
Starting from microcanonical basis with the principle of equal a priori probability, it is found that, besides ordinary Boltzmann-Gibbs theory with the exponential distribution, a…