Tsallis q-exponential distributions arise by minimizing a free energy built from a self-consistency entropy defined via a nonlinear operator Omega, with q = alpha + beta obtained directly from the operator's fixed-point structure.
Nonextensive thermodynamic relations
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Proves an H-theorem for monotonic decrease of a convex functional under iteration and gradient flow of a self-referential operator Omega within the local kernel approximation, with perturbative stability of the Tsallis index and numerical confirmation of a re-entrant disordered phase at kappa > 0.5.
Derives q-dependent momentum distribution and non-zero correlations for free particles in Tsallis statistics using physical temperature, valid for 1-1/(3N/2+1) < q < 1.
citing papers explorer
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Emergence of Tsallis Statistics from a Self-Referential Nonlinear Operator: A Variational Framework
Tsallis q-exponential distributions arise by minimizing a free energy built from a self-consistency entropy defined via a nonlinear operator Omega, with q = alpha + beta obtained directly from the operator's fixed-point structure.
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Irreversibility from Self-Reference: Gradient Flow and an H-Theorem for a Self-Referential Statistical Operator Framework
Proves an H-theorem for monotonic decrease of a convex functional under iteration and gradient flow of a self-referential operator Omega within the local kernel approximation, with perturbative stability of the Tsallis index and numerical confirmation of a re-entrant disordered phase at kappa > 0.5.
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Momentum distribution and correlation function of free particles in the Tsallis statistics using conventional expectation value and equilibrium temperature
Derives q-dependent momentum distribution and non-zero correlations for free particles in Tsallis statistics using physical temperature, valid for 1-1/(3N/2+1) < q < 1.