Connections between Tsallis' formalisms employing the standard linear average energy and ones employing the normalized $q$-average energy

Abstract

Tsallis' thermostatistics with the standard linear average energy is revisited by employing $S_{2-q}$, which is the Tsallis entropy with $q$ replaced by $2-q$. We explore the connections among the $S_{2-q}$ approach and the other different versions of Tsallis formalisms. It is shown that the normalized $q$-average energy and the standard linear average energy are related to each other. The relations among the Lagrange multipliers of the different versions are revealed. The relevant Legendre transform structures concerning the Lagrange multipliers associated with the normalization of probability are studied. It is shown that the generalized Massieu potential associated with $S_{2-q}$ and the linear average energy is related to one associated with the normalized Tsallis entropy and the normalized $q$-average energy.

16 pages, no figure, submitted to Physics Letter A

References in corpus (16)

• Nonextensive thermodynamic relations
• Two-parameter deformations of logarithm, exponential, and entropy: A consistent framework for generalized statistical mechanics
• Nonextensive statistical mechanics: A brief introduction
• Tsallis' entropy maximization procedure revisited
• Nonextensive Pesin identity. Exact renormalization group analytical results for the dynamics at the edge of chaos of the logistic map
• Deformed exponentials and logarithms in generalized thermostatistics
• Implications of Form Invariance to the Structure of Nonextensive Entropies
• Deformed logarithms and entropies
• Generalized thermostatistics based on deformed exponential and logarithmic functions
• Generalized entropy optimized by an arbitrary distribution
• Ideal gas in nonextensive optimal Lagrange multipliers formalism
• Thermodynamics' 0-th-Law in a nonextensive scenario
• Generalized thermostatistics and mean-field theory
• On the robust thermodynamical structures against arbitrary entropy form and energy mean value
• Some thoughts on theoretical physics
• Constraints and relative entropies in nonextensive statistical mechanics

Cited by in corpus (21)

• Numerical indications of a q-generalised central limit theorem
• Entropic Forms and Related Algebras
• Dual Conformable Derivative: Definition, Simple Properties and Perspectives for Applications
• A non self-referential expression of Tsallis' probability distribution function
• Legendre structure of the thermostatistics theory based on the Sharma-Taneja-Mittal entropy
• Geometric study for the Legendre duality of generalized entropies and its application to the porous medium equation
• Multiplicative duality, q-triplet and (mu,nu,q)-relation derived from the one-to-one correspondence between the (mu,nu)-multinomial coefficient and Tsallis entropy Sq
• Escort entropies and divergences and related canonical distribution
• Long-range interactions, doubling measures and Tsallis entropy
• Equivalence among different formalisms in the Tsallis entropy framework
• Intensive variables in the framework of the non-extensive thermostatistics
• Information Geometry of q-Gaussian Densities and Behaviors of Solutions to Related Diffusion Equations
• On the equivalence between four versions of thermostatistics based on strongly pseudo-additive entropies
• Non-extensive thermostatistics approach to metal melting entropy
• $\alpha$-divergence derived as the generalized rate function in a power-law system
• Dually flat structure with escort probability and its application to alpha-Voronoi diagrams
• On Measure Theoretic definitions of Generalized Information Measures and Maximum Entropy Prescriptions
• Exponential or power law? How to select a stable distribution of probability in a physical system
• On Shore and Johnson properties for a Special Case of Csiszár f-divergences
• Linearization Principle: The Geometric Origin of Nonlinear Fokker-Planck Equations
• The Boltzmann temperature and Lagrange multiplier