Generalized Boltzmann factors induced by Weibull-type distributions

• Published in: Physica A Vol. 392; no. 4; pp. 545 - 551
• Main Authors: Mathai, A.M., Provost, Serge B.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.02.2013
• Subjects: Boltzmann factor; Complement; Dynamical systems; Dynamics; Exact solutions; Generalized gamma distribution; Inverse; Inverse Mellin transform; Joints; Mathematical analysis; Mathematical models; Statistical thermodynamics; Superstatistics; Tsallis’ statistics; Weibull distribution; Statistical thermodynamics; Superstatistics; Inverse Mellin transform; Tsallis’ statistics; Boltzmann factor; Weibull distribution; Generalized gamma distribution
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2012.10.030

The inverse Mellin transform technique is utilized to obtain closed form representations of the generalized Boltzmann factors associated with several Weibull-type models such as the generalized gamma, Maxwell, Rayleigh and half-normal distributions. The results complement those already available in the Physics literature in connection with the distribution of certain variables affecting the behavior of nonequilibrium systems subject to complex dynamics, which include for instance computable expressions for the generalized Boltzmann factors induced by the gamma, F, uniform and lognormal statistical models. ► Generalized Boltzmann factors associated with Weibull-type densities are provided. ► Particular cases include the Weibull, Maxwell, half-normal and Rayleigh densities. ► Representations in terms of generalized hypergeometric functions are obtained.