Matsoukas T. Generalized Statistical Thermodynamics: Thermodynamics of Probability Distributions and Stochastic Processes

Springer, 2018. — 373 p. — (Understanding Complex Systems). — ISBN: 978-3-030-04148-9.This book gives the definitive mathematical answer to what thermodynamics really is: a variational calculus applied to probability distributions. Extending Gibbs's notion of ensemble, the Author imagines the ensemble of all possible probability distributions and assigns probabilities to them by selection rules that are fairly general. The calculus of the most probable distribution in the ensemble produces the entire network of mathematical relationships we recognize as thermodynamics.
The first part of the book develops the theory for discrete and continuous distributions while the second part applies this thermodynamic calculus to problems in population balance theory and shows how the emergence of a giant component in aggregation, and the shattering transition in fragmentation may be treated as formal phase transitions.
While the book is intended as a research monograph, the material is self-contained and the style sufficiently tutorial to be accessible for self-paced study by an advanced graduate student in such fields as physics, chemistry, and engineering.Evolution of Ideas on Entropy
The Cluster Ensemble
Thermodynamic Limit (ThL)
The Most Probable Distribution in the Continuous Limit
Phase Transitions: The Giant Cluster
The Bicomponent Ensemble
Generalized Thermodynamics
Irreversible Clustering
Kinetic Gelation
Fragmentation and Shattering