VERIFICATIONS AND APPLICATIONS
(a selection)

Theoretical

1. C. Tsallis, D.J. Bukman
Anomalous diffusion in the presence of external forces: Exact time-dependent solutions and their thermostatistical basis
Physical Review E 54, R2197-R2200 (1996)


2. R.J.V. dos Santos
Generalization of Shannon’s theorem for Tsallis entropy
Journal of Mathematical Physics 38, 4104-4107 (1997)


3. M.L. Lyra, C. Tsallis
Nonextensivity and multifractality in low-dimensional dissipative systems
Physical Review Letters 80, 53-56 (1998)


4. S. Abe

Axioms and uniqueness theorem for Tsallis entropy
Physics Letters A 271, 74–79 (2000)


5. C. Beck, E.G.D. Cohen
Superstatistics
Physica A 322, 267–275 (20003)


6. F. Baldovin, A. Robledo
Nonextensive Pesin identity: Exact renormalization group analytical results for the dynamics at the edge of chaos of the logistic map
Physical Review E 69, 045202(R) (2004)


7. C. Tsallis, M. Gell-Mann, Y. Sato
Asymptotically scale-invariant occupancy of phase space makes the entropy Sq extensive
Proceedings of the National Academy of Sciences (USA) 102, 15377-15382 (2005)


8. S. Umarov, C. Tsallis, S. Steinberg
On a q-Central Limit Theorem consistent with nonextensive statistical mechanics
Milan Journal of Mathematics 76, 307–328 (2008)


9. A. Rodriguez, V. Schwammle, C. Tsallis
Strictly and asymptotically scale invariant probabilistic models of N correlated binary random variables having Gaussians as N →∞ limiting distributions
Journal of Statistical Mechanics: Theory and Experiment 09, P09006 (2008)


10. F. Caruso, C. Tsallis
Nonadditive entropy reconciles the area law in quantum systems with classical thermodynamics
Physical Review E 78, 021102 (2008)


11. M.A. Fuentes, M.O. Cáceres
Computing the non-linear anomalous diffusion equation from first principles
Physics Letters A 372, 1236–1239 (2008)


12. R. Hanel, S. Thurner, C. Tsallis
Limit distributions of scale-invariant probabilistic models of correlated random variables with the q-Gaussian as an explicit example
European Physical Journal B 72, 263-268 (2009)


13. S. Umarov, C. Tsallis, M. Gell-Mann, S. Steinberg
Generalization of symmetric alpha-stable Lévy distributions for q>1

Journal of Mathematical Physics 51, 033502 (2010)


14. J.S. Andrade, Jr., G.F.T. da Silva, A.A. Moreira, F.D. Nobre, E.M.F. Curado
Thermostatistics of Overdamped Motion of Interacting Particles
Physical Review Letters 105, 260601 (2010)


15. F.D. Nobre, M.A. Rego-Monteiro, C. Tsallis
Nonlinear Relativistic and Quantum Equations with a Common Type of Solution
Physical Review Letters 106, 140601 (2011)


16. M. Jauregui, C. Tsallis
New representations of pi and Dirac delta using the nonextensive-statistical-mechanics q-exponential function
Journal of Mathematical Physics 51, 063304 (2010)


17. M. Jauregui, C. Tsallis
q-Generalization of the inverse Fourier transform
Physics Letters A 375, 2085–2088 (2011)


18. P. Tempesta
Group entropies, correlation laws, and zeta functions
Physical Review E 84, 021121 (2011)


19. M. Jauregui, C. Tsallis, E.M.F. Curado
q-moments remove the degeneracy associated with the inversion of the q-Fourier transform
Journal of Statistical Mechanics: Theory and Experiment 11, 1742-5468 (2011)


20. R. Hanel, S. Thurner
When do generalized entropies apply? How phase space volume determines entropy
Europhysics Letters 96, 50003 (2011)


21. R. Hanel, S. Thurner, M. Gell-Mann
Generalized entropies and the transformation group of superstatistics
Proceedings of the National Academy of Sciences, 1103539108 (2011)


22. C. Vignat, A. Plastino, A.R. Plastino, J.S. Dehesa
Quantum potentials with q-Gaussian ground states
Physica A 391, 1068-1073 (2012)


23. M.S. Ribeiro, F.D. Nobre, E.M.F. Curado
Time evolution of interacting vortices under overdamped motion
Physical Review E 85, 021146 (2012)


24. B. Luque, L. Lacasa, A. Robledo
Feigenbaum graphs at the onset of chaos
Physics Letters A 376, 3625–3629 (2012)


25. J.F. Bercher
On multidimensional generalized Cramér–Rao inequalities, uncertainty relations and characterizations of generalized q-Gaussian distributions
Journal of Physics A: Mathematical and Theoretical 46, 095303 (2013)


26. C. Tsallis, L. J. L. Cirto
Black hole thermodynamical entropy
The European Physical Journal C 73, 2487 (2013)


27. B. A. Mello, D. O. Cajueiro
A note on the connection between the Tsallis' thermodynamics and cumulative prospect theory
Revista Brasileira de Economia de Empresas 10(1), 31-36 (2013)


28. H. Bergeron, E. M. F. Curado, J. P. Gazeau, Ligia M. C. S. Rodrigues
Symmetric generalized binomial distributions
Journal of Mathematical Physics 54, 123301 (2013)


29. E. M. F. Curado, A. M. C. Souza, F. D. Nobre, R. F. S. Andrade
Carnot cycle for interacting particles in the absence of thermal noise
Physical Review E 89, 022117 (2014)


30. Z. González Arenas, D. G. Barci, C. Tsallis
Nonlinear inhomogeneous Fokker-Planck equation within a generalized Stratonovich prescription
Physical Review E 90, 032118 (2014)


31. R. F. S. Andrade, A. M. C. Souza, E. M. F. Curado and F. D. Nobre
A thermodynamical formalism describing mechanical interactions
Physical Review E 90, 032118 (2014)


32. M. S. Ribeiro, G. A. Casas, F. D. Nobre
Second law and entropy production in a nonextensive system
Physical Review E 91, 012140 (2015)


33. F. D. Nobre, E. M. F. Curado, A. M. C. Souza, R. F. S. Andrade
Consistent thermodynamic framework for interacting particles by neglecting thermal noise
Physical Review E 91, 022135 (2015)


34. C. Tsallis, H. J. Haubold
Boltzmann-Gibbs entropy is sufficient but not necessary for the likelihood factorization required by Einstein
EPL 110, 30005 (2015)


35. C. M. Vieira, H. A. Carmona, J. S. Andrade Jr., A. A. Moreira
General continuum approach for dissipative systems of repulsive particles
Physical Review E 93, 060103 (2016)


36. S. Umarov, C. Tsallis
The limit distribution in the q-CLT for q≥1 is unique and can not have a compact support
Journal of Physics A: Mathematical and Theoretical 49, 415204 (2016)


37. R. S. Wedemann, A. R. Plastino, C. Tsallis
Curl forces and the nonlinear Fokker-Planck equation
Physical Review E 94, 062105 (2016)


38. G. Sicuro, P. Rapcan, C. Tsallis
Nonlinear inhomogeneous Fokker-Planck equations: Entropy and free-energy time evolution
Physical Review E 94, 062117 (2016)



Group of
Statistical Physics
(CBPF)
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