© 2011

Generalised Thermostatistics

  • This book is the first to present the recent progress in generalising the well-established idioms of statistical physics

  • Theory is supplemented with pointers to application-based references

  • Provides readers with the opportunity to learn in a systematic manner about q-deformed exponential and logarithmic functions, their role in Tsallis' nonextensive thermostatistics, and how everything fits into a more general mathematical formalism


Table of contents

  1. Front Matter
    Pages I-X
  2. Parameter Estimation

    1. Front Matter
      Pages 1-2
    2. Jan Naudts
      Pages 21-36
    3. Jan Naudts
      Pages 37-51
    4. Jan Naudts
      Pages 53-68
    5. Jan Naudts
      Pages 69-78
    6. Jan Naudts
      Pages 79-92
  3. Deformed Exponential Families

    1. Front Matter
      Pages 93-94
    2. Jan Naudts
      Pages 95-114
    3. Jan Naudts
      Pages 115-130
    4. Jan Naudts
      Pages 131-148
    5. Jan Naudts
      Pages 149-163
    6. Jan Naudts
      Pages 165-178
  4. Jan Naudts
    Pages 179-198
  5. Back Matter
    Pages 199-201

About this book


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

Authors and affiliations

  1. 1.Physics DepartmentUniversity of AntwerpAntwerpBelgium

Bibliographic information

Industry Sectors
Finance, Business & Banking


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)