物理学における確率：基礎と応用（テキスト） Probability in Physics : Foundations and Applications

著者名：Boffetta, Guido/Vulpiani, Angelo

Springer（2026/02/10発売）

• 言語：ENG
• ISBN：9783032104069
• eISBN：9783032104076

Description

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.

Table of Contents

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.