Generalised Thermostatistics

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.

• Exponential family of statistical models
• Microcanonical ensemble
• Nonextensive thermostatistics
• Tsallis entropy
• q-deformed exponential functions
• q-deformed logarithmic functions

From the reviews:

“This book is written in such a manner that it presents some aspects of generalized thermostatics by a very wide context of considerations. … It is introduced in a very interesting way, leading the reader to more and more general approaches. … Step-by-step, the ideas for different generalizations are presented. … Each chapter of the book ends with some problems intended for a better understanding of the presented topics. At the end of the book, the reader can find the solutions to these problems.” (Dominik Strzałka, Zentralblatt MATH, Vol. 1231, 2012)

“This book addresses fundamental issues of thermostatistics from the point of view of statistics applied to physics. Many subtle aspects of the theory that are not usually emphasised in standard textbooks are discussed, and the reader can benefit from a deeper understanding of the subject. … The book can be used in an advanced course for graduate students, and it is also useful for researchers in statistical physics, since it deals with many aspects of current developments.” (Ernesto P. Borges, Mathematical Reviews, Issue 2012 h)

• Physics Department, University of Antwerp, Antwerp, Belgium

  Jan Naudts

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