This textbook aims to bridge a longstanding gap by presenting a rigorous yet physics-centered approach to probability theory and its applications. Despite its foundational role across nearly all areas of physics, many students exhibit notable technical and conceptual gaps in even the most basic aspects of probability. Surprisingly, these issues can persist even among those specializing in statistical mechanics.

According to the authors, these shortcomings are largely a consequence of how probability is taught within the physics curriculum. Typically, core concepts are introduced early in a fragmented way, often within laboratory courses, and receive only cursory treatment in statistical mechanics classes. In contrast, more comprehensive and mathematically rigorous instruction is usually reserved for advanced graduate-level courses, which often lack a strong connection to physical intuition.

This book addresses that imbalance by offering a cohesive and accessible framework tailored to the needs of physics students.

Provides a comprehensive introduction to probability theory Explores the use of probability theory in physical problems Traces the path from elementary probability theory to its application in statistical physics

Autorentext
Guido Boffetta is full professor in Theoretical physics of condensed matter at the University of Torino. His research interests cover Dynamical systems, Turbulence theory, Stochastic processes, Numerical methods. He is author of more than 150 scientific papers and has an impact index h=54 (Google scholar). Angelo Vulpiani is professor in Theoretical physics at the University of Rome "Sapienza". His research interests cover Statistical mechanics, Chaos, Turbulence theory. He is author of about 200 scientific papers and 12 books and has an impact index h=69 (Google scholar).

Inhalt

Introduction.- Some Results with a Bit of Formalism.- Limit Theorems The Statistical Behavior of Systems with Many Variables.- Brownian Motion First Encounter with Stochastic Processes.- Discrete Stochastic Processes Markov Chains.- Stochastic Processes with Continuous States and Time.- Probability and Deterministic Chaotic Systems.- Beyond the Gaussian Distribution.- Entropy Information and Chaos.- Appendix: Some Useful Results and Complements.