[1]
|
C. Tsallis, “Possible Generalization of Boltzmann-Gibbs Statistics,” Journal of Statistical Physics, Vol. 52, No. 1-2, 1988, pp. 479-487. doi:10.1007/BF01016429
|
[2]
|
P. H. Chavanis, “Generalized Thermodynamics and Fokker-Planck Equations: Applications to Stellar Dynamics and Two-Dimensional Turbulence,” Physical Review E, Vol. 68, No. 3, 2003, pp. 036108-036127.
doi:10.1103/PhysRevE.68.036108
|
[3]
|
P. H. Chavanis, “Nonlinear Mean Field Fokker-Planck Equations. Application to the Chemotaxis of Biological Populations,” The European Physical Journal B—Condensed Matter and Complex Systems, Vol. 62, 2008, pp. 179-208.
|
[4]
|
P. H. Chavanis, “Generalized Fokker-Planck Equations and Effective Thermodynamics,” Physica A: Statistical Mechanics and Its Applications, Vol. 340, 2004, pp. 57- 65.
|
[5]
|
P. H. Chavanis and M. Lemou, “Relaxation of the Distribution Function Tails for Systems Described by Fokker-Planck Equations,” Physical Review E, Vol. 72, No. 6, 2005, pp. 061106-061121.
doi:10.1103/PhysRevE.72.061106
|
[6]
|
P. H. Chavanis, “Nonlinear Mean-Field Fokker-Planck Equations and Their Applications in Physics, Astrophysics and Biology,” Comptes Rendus Physique, Vol. 7, No. 3, 2006, pp. 318-330. doi:10.1016/j.crhy.2006.01.004
|
[7]
|
V. Schw?mmle, E. M.F. Curado and F. D. Nobre, “A General Nonlinear Fokker-Planck Equation and Its Associated Entropy,” The European Physical Journal B— Condensed Matter and Complex Systems, Vol. 58, 2007, pp. 159-165.
|
[8]
|
V. Schw?mmle, F. D. Nobre and E. M. F. Curado, “Consequences of the H Theorem from Nonlinear Fokker- Planck Equations,” Physical Review E, Vol. 76, No. 4, 2007, pp. 041123-041130.
doi:10.1103/PhysRevE.76.041123
|
[9]
|
V. Schw?mmle, E. M. F. Curado and F. D. Nobre, “Dynamics of Normal and Anomalous Diffusion in Nonlinear Fokker-Planck Equations,” The European Physical Jour- nal B—Condensed Matter and Complex Systems, Vol. 70, 2009, pp. 107-116.
|
[10]
|
V. Schw?mmle, E. M.F. Curado and F. D. Nobre, “Non- linear Fokker-Planck Equations Related to Standard Ther- mostatistics,” Complexity, Metastability and Nonextensivity, Vol. 84, 2007, pp. 152-156.
|
[11]
|
M. S. Ribeiro, F. D. Nobre and E. M. F. Curado, “Classes of N-Dimensional Nonlinear Fokker-Planck Equations Associated to Tsallis Entropy,” Entropy, Vol. 13, No. 11, 2011, pp. 1928-1944. doi:10.3390/e13111928
|
[12]
|
A. M. Scarfone and T. Wada, “Lie Symmetries and Related Group-Invariant Solutions of a Nonlinear Fokker- Planck Equation Based on the Sharma-Taneja-Mittal Entropy,” Brazilian Journal of Physics, Vol. 30, No. 2A, 2009. doi:10.1590/S0103-97332009000400024
|
[13]
|
T. D. Frank, A. Daffertshofer, C. E. Peper, P. J. Beek and H. Haken, “Towards a Comprehensive Theory of Brain Activity: Coupled Oscillator Systems under External Forces,” Physica D: Nonlinear Phenomena, Vol. 144, No. 1-2, 2000, pp. 62-86.
doi:10.1016/S0167-2789(00)00071-3
|
[14]
|
T. D. Frank, A. Daffertshofer and P. J. Beek, “Multivariate Ornstein-Uhlenbeck Processes with Mean-Field Dependent Coefficients: Application to Postural Sway,” Physical Review E, Vol. 63, No. 1, 2000, pp. 011905- 011920. doi:10.1103/PhysRevE.63.011905
|
[15]
|
T. D. Frank and A. Daffertshofer, “Exact Time-Depen- dent Solutions of the Renyi Fokker-Planck Equation and the Fokker-Planck Equations Related to the Entropies Proposed by Sharma and Mittal,” Physica A: Statistical Mechanics and Its Applications, Vol. 285, 2000, pp. 351-366.
|
[16]
|
T. D. Frank, “On Nonlinear and Nonextensive Diffusion and the Second Law of Thermodynamics,” Physics Letters A, Vol. 267, No. 5-6, 2000, pp. 298-304.
doi:10.1016/S0375-9601(00)00127-4
|
[17]
|
A. Daffertshofer, C. E. Peper, T. D. Frank and P. J. Beek, “Spatio-Temporal Patterns of Encephalographic Signals during Polyrhythmic Tapping,” Human Movement Science, Vol. 19, No. 4, 2000, pp. 475-498.
doi:10.1016/S0167-9457(00)00032-4
|
[18]
|
A.R. Plastino and A. Plastino, “Non-Extensive Statistical Mechanics and Generalized Fokker-Planck Equation,” Physica A: Statistical Mechanics and Its Applications, Vol. 222, 1995, pp. 347-354.
|
[19]
|
A.R. Plastino, A. Plastino and H. Vucetich, “A Quantitative Test of Gibbs’ Statistical Mechanics,” Physics Letters A, Vol. 207, No. 1-2, 1995, pp. 42-46.
doi:10.1016/0375-9601(95)00640-O
|
[20]
|
F. Pennini, A. Plastino and A.R. Plastino, “Tsallis Entropy and Quantal Distribution Functions,” Physics Letters A, Vol. 208, No. 4-6, 1995, pp. 309-314.
doi:10.1016/0375-9601(95)00720-1
|
[21]
|
A. R. Plastino and A. Plastino, “Fisher Information and Bounds to the Entropy Increase,” Physical Review E, Vol. 52, No. 4, 1995, pp. 4580-4582.
doi:10.1103/PhysRevE.52.4580
|
[22]
|
M. Portesi, A. Plastino and C. Tsallis, “Nonextensive Thermostatistics Can Yield Apparent Magnetism,” Physical Review E, Vol. 52, 1995, pp. R.3317-R.3320.
|
[23]
|
T. D. Frank, “Stochastic Feedback, Nonlinear Families of Markov Processes, and Nonlinear Fokker-Planck Equations,” Physica A: Statistical Mechanics and Its Applications, Vol. 331, 2004, pp. 391-408.
|
[24]
|
T. D. Frank, “Analytical Results for Fundamental Time- Delayed Feedback Systems Subjected to Multiplicative Noise,” Physical Review E, Vol. 69, No. 6, 2004, pp. 061104-061114. doi:10.1103/PhysRevE.69.061104
|
[25]
|
T. D. Frank, “Fluctuation-Dissipation Theorems for Non- linear Fokker-Planck Equations of the Desai-Zwanzig Type and Vlasov-Fokker-Planck Equations,” Physics Letters A, Vol. 329, No. 6, 2004, pp. 475-485.
doi:10.1016/j.physleta.2004.07.019
|
[26]
|
T. D. Frank, “Classical Langevin Equations for the Free Electron Gas and Blackbody Radiation,” Journal of Physics A: Mathematical and General, Vol. 37, No. 11, 2004, p. 3561. doi:10.1088/0305-4470/37/11/001
|
[27]
|
T. D. Frank, P. J. Beek and R. Friedrich, “Identifying Noise Sources of Time-Delayed Feedback Systems,” Physics Letters A, Vol. 328, No. 2-3, 2004, pp. 219-224.
doi:10.1016/j.physleta.2004.06.012
|
[28]
|
T. D. Frank, “Stability Analysis of Stationary States of Mean Field Models Described by Fokker-Planck Equations,” Physica D: Nonlinear Phenomena, Vol. 189, No. 3-4, 2004, pp. 199-218. doi:10.1016/j.physd.2003.08.010
|
[29]
|
T. D. Frank, “Complete Description of a Generalized Ornstein-Uhlenbeck Process Related to the Nonextensive Gaussian Entropy,” Physica A: Statistical Mechanics and its Applications, Vol. 340, 2004, pp. 251-256.
|
[30]
|
T. D. Frank, “Dynamic Mean Field Models: H-Theorem for Stochastic Processes and Basins of Attraction of Stationary Processes,” Physica D: Nonlinear Phenomena, Vol. 195, No. 3-4, 2004, pp. 229-243.
doi:10.1016/j.physd.2004.03.014
|
[31]
|
T. D. Frank, “Nonlinear Fokker-Plank Equations,” Springer, Amsterdam, 2004.
|
[32]
|
A. M. Mathai and H. J. Haubold, “On Generalized Entropy Measures and Pathways,” Physica A: Statistical Mechanics and Its Applications, Vol. 385, 2007, pp. 493- 500.
|
[33]
|
T. D. Frank and A. R. Plastino, “Generalized Thermostatistics Based on the Sharma-Mittal Entropy and Escort Mean Values,” The European Physical Journal B— Condensed Matter and Complex Systems, Vol. 30, 2002, pp. 543-549.
|
[34]
|
T. D. Frank, “Generalized Fokker-Planck Equations Derived from Generalized Linear Nonequilibrium Thermo- dynamics,” Physica A: Statistical Mechanics and Its Applications, Vol. 310, 2002, pp. 397-412.
|
[35]
|
T. D. Frank, “On a General Link between Anomalous Diffusion and Nonextensivity,” Journal of Mathematical Physics, Vol. 43, No. 1, 2002, pp. 344-350.
doi:10.1063/1.1421062
|
[36]
|
T. D. Frank, “Generalized Multivariate Fokker-Planck Equations Derived from Kinetic Transport Theory and Linear Nonequilibrium Thermodynamics,” Physics Letters A, Vol. 305, No. 3-4, 2002, pp. 150-159.
doi:10.1016/S0375-9601(02)01446-9
|
[37]
|
T. D. Frank, “Interpretation of Lagrange Multipliers of Generalized Maximum-Entropy Distributions,” Physics Letters A, Vol. 299, 2002, pp. 153-158.
doi:10.1016/S0375-9601(02)00631-X
|
[38]
|
T. D. Frank, A. Daffertshofer and P. J. Beek, “Impacts of Statistical Feedback on the Flexibility-Accuracy Trade- Offin Biological Systems,” Journal of Biological Physics, Vol. 28, No. 2-3, 2002, pp. 39-54.
doi:10.1023/A:1016256613673
|