Conservative Force Fields in Non-Gaussian Statistics

Abstract In this Letter, we determine the κ-distribution function for a gas in the presence of an external field of force described by a potential U ( r ) . In the case of a dilute gas, we show that the κ-power law distribution including the potential energy factor term can rigorously be deduced in the framework of kinetic theory with basis on the Vlasov equation. Such a result is significant as a preliminary to the discussion on the role of long range interactions in the Kaniadakis thermostatistics and the underlying kinetic theory.

[1]  Bin Liu,et al.  Superdiffusion and non-Gaussian statistics in a driven-dissipative 2D dusty plasma. , 2008, Physical review letters.

[2]  Non-extensive statistics and the stellar polytrope index , 2004, astro-ph/0402245.

[3]  Relativity, nonextensivity, and extended power law distributions. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  A Maxwellian path to the q-nonextensive velocity distribution function , 1998, cond-mat/0201503.

[5]  Canonical quantization of nonlinear many-body systems. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  A M Scarfone,et al.  Two-parameter deformations of logarithm, exponential, and entropy: a consistent framework for generalized statistical mechanics. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Negative heat capacity and non-extensive kinetic theory , 2003, astro-ph/0306009.

[8]  Transport coefficients and nonextensive statistics , 2002, cond-mat/0201541.

[9]  J. Lima,et al.  Plasma oscillations and nonextensive statistics , 2000 .

[10]  H. G. Miller,et al.  κ-DEFORMED STATISTICS AND THE FORMATION OF A QUARK-GLUON PLASMA , 2003 .

[11]  P. Douglas,et al.  Tunable Tsallis distributions in dissipative optical lattices. , 2006, Physical review letters.

[12]  Masa-aki Sakagami,et al.  Gravothermal catastrophe and generalized entropy of selfgravitating systems , 2001 .

[13]  R. Silva,et al.  Nonextensive models for earthquakes. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  A. M. Scarfone,et al.  A new one-parameter deformation of the exponential function , 2002 .

[15]  T S Biró,et al.  Nonextensive boltzmann equation and hadronization. , 2005, Physical review letters.

[16]  Galaxy luminosity function: a new analytic expression , 2004 .

[17]  A. M. Scarfone,et al.  Deformed logarithms and entropies , 2004, cond-mat/0402418.

[18]  G. Kaniadakis,et al.  Non-linear kinetics underlying generalized statistics , 2001 .

[19]  Denis Bolduc,et al.  The K-deformed multinomial logit model , 2005 .

[20]  R. Silva,et al.  The H-theorem in κ-statistics : influence on the molecular chaos hypothesis , 2006 .

[21]  R. Silva.  The relativistic statistical theory and Kaniadakis entropy: an approach through a molecular chaos hypothesis , 2006 .

[22]  Radial velocities of open stellar clusters: a new solid constraint favouring Tsallis maximum entropy theory , 2007 .

[23]  A. M. Scarfone,et al.  Generalized kinetic equations for a system of interacting atoms and photons: theory and simulations , 2004 .

[24]  C. Tsallis,et al.  Nonextensive Entropy: Interdisciplinary Applications , 2004 .

[25]  J. Lima,et al.  The nonextensive gas: a kinetic approach , 2005 .

[26]  Sumiyoshi Abe,et al.  Stabilities of generalized entropies , 2004 .

[27]  P. Chavanis.  Gravitational instability of isothermal and polytropic spheres , 2002, astro-ph/0207080.

[28]  Power-law stellar distributions , 2004, astro-ph/0406404.

[29]  J. Lima,et al.  Jeans' gravitational instability and nonextensive kinetic theory , 2001, astro-ph/0109474.

[30]  G. Kaniadakis.  H-theorem and generalized entropies within the framework of nonlinear kinetics , 2001 .

[31]  A. Plastino,et al.  Nonextensive thermostatistics and the H theorem. , 2001, Physical review letters.

[32]  E. M.,et al.  Statistical Mechanics , 2021, Manual for Theoretical Chemistry.

[33]  J. Alcaniz,et al.  Nonextensive effects on the relativistic nuclear equation of state , 2007, 0705.0300.

[34]  Conservative force fields in nonextensive kinetic theory , 2002, cond-mat/0210039.

[35]  G. Kaniadakis,et al.  Statistical mechanics in the context of special relativity. II. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  P. Chavanis.  Gravitational instability of polytropic spheres and generalized thermodynamics , 2001, astro-ph/0108378.

[37]  Du Jiulin,et al.  The nonextensive parameter and Tsallis distribution for self-gravitating systems , 2004 .

[38]  C. Tsallis,et al.  Nonergodicity and central-limit behavior for long-range Hamiltonians , 2007, 0706.4021.

[39]  MASS FUNCTION OF HALOS: A NEW ANALYTICAL APPROACH , 2004 .

[40]  Antal Jakovác,et al.  Power-law tails from multiplicative noise. , 2005, Physical review letters.

[41]  Masatoshi Shiino,et al.  Stability analysis of mean-field-type nonlinear Fokker-Planck equations associated with a generalized entropy and its application to the self-gravitating system. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  N. A. Krall,et al.  Principles of Plasma Physics , 1973 .

[43]  A. M. Scarfone,et al.  Kinetical foundations of non-conventional statistics , 2001 .

[44]  J. Lima,et al.  Press-Schechter Mass Function and the Normalization Problem , 2007 .

[45]  O. Høst,et al.  Impact of going beyond the Maxwell distribution in direct dark matter detection rates , 2007, 0711.4895.

[46]  Equipartition and virial theorems within general thermostatistical formalisms , 1999 .

[47]  Giorgio Kaniadakis,et al.  A κ-entropic approach to the analysis of the fracture problem , 2004 .

[48]  Bartłomiej Dybiec,et al.  Resonant activation in the presence of nonequilibrated baths. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  Long-term evolution of stellar self-gravitating systems away from thermal equilibrium: connection with nonextensive statistics. , 2003, Physical review letters.

[50]  T. Kodama,et al.  Dynamical correlations as origin of nonextensive entropy , 2005 .

[51]  A. M. Scarfone,et al.  Lesche stability of κ-entropy , 2004 .

[52]  C. Tsallis.  Possible generalization of Boltzmann-Gibbs statistics , 1988 .

[53]  Jeans' criterion and nonextensive velocity distribution function in kinetic theory , 2004 .

[54]  S. Abe,et al.  Nonextensive Statistical Mechanics and Its Applications , 2010 .