Generalised Thermostatistics - Naudts, Jan.; SpringerLink (Online service) (London : Springer London, 2011)
The domain of non-extensive thermostatistics has been subject to intensive research over the past twenty years and has matured significantly. Generalised Thermostatistics cuts through the traditionalism of many statistical physics texts by offering a fresh perspective and seeking to remove elements of doubt and confusion surrounding the area. The book is divided into two parts - the first covering topics from conventional statistical physics, whilst adopting the perspective that statistical physics is statistics applied to physics. The second developing the formalism of non-extensive thermostatistics, of which the central role is played by the notion of a deformed exponential family of probability distributions. Presented in a clear, consistent, and deductive manner, the book focuses on theory, part of which is developed by the author himself, but also provides a number of references towards application-based texts. Written by a leading contributor in the field, this book will provide a useful tool for learning about recent developments in generalized versions of statistical mechanics and thermodynamics, especially with respect to self-study. Written for researchers in theoretical physics, mathematics and statistical mechanics, as well as graduates of physics, mathematics or engineering. A prerequisite knowledge of elementary notions of statistical physics and a substantial mathematical background are required.
Parameter estimation -- Statistical Models -- Thermodynamic Equilibrium -- The Microcanonical Ensemble -- Hyperensembles -- The Mean Field Approximation -- q-Deformed Distributions -- Tsallis$1 (BThermostatistics -- Changes of Scale -- General deformations -- General Entropies.s
Keywords: Mathematics; Mathematical physics; Thermodynamics; Mathematics; Mathematics, general; Statistical Physics, Dynamical Systems and Complexity; Mathematical Methods in Physics; Thermodynamics