作者陳木法先生是北京師范大學教授，中科院院士。作者最先從非平衡統計物理中引進無窮維反應擴散過程，解決了過程的構造、平衡態的存在性和唯一性等根本課題，此方向今已成為國際上粒子系統研究的重要分支。書中主要闡述概率論及其在物理學中的應用，全書分為4部分，16章。

Preface to the First EditionPreface to the Second EditionChapter 0. An Overview of the Book:Starting From Markov Chains0.1. Three Classical Problems for Markov Chains0.2. Probability Metrics and Coupling Methods0.3. Reversible Markov Chains0.4. Large Deviations and Spectral Gap0.5. Equilibrium Particle Systems0.6. Non-equilibrium Particle SystemsPart Ⅰ. General Jump ProcessesChapter 1. Transition Function and its Laplace Transform1.1. Basic Properties of Transition Function1.2. The q-Pair1.3. Differentiability1.4. Laplace Transforms1.5. Appendix1.6. NotesChapter 2. Existence and Simple Constructions of Jump Processes2.1. Minimal Nonnegative Solutions2.2. Kolmogorov Equations and Minimal Jump Process2.3. Some Sufficient Conditions for Uniqueness2.4. Kolmogorov Equations and q-Condition2.5. Entrance Space and Exit Space2.6. Construction of q-Processes with Single-Exit q-Pair2.7. NotesChapter 3. Uniqueness Criteria3.1. Uniqueness Criteria Based on Kolmogorov Equations3.2. Uniqueness Criterion and Applications3.3. Some Lemmas3.4. Proof of Uniqueness Criterion3.5. NotesChapter 4. Recurrence, Ergodicity and Invariant Measures4.1. Weak Convergence4.2. General Results4.3. Markov Chains: Time-discrete Case4.4. Markov Chains: Time-continuous Case4.5. Single Birth Processes4.6. Invariant Measures4.7. NotesChapter 5. Probability Metrics and Coupling Methods5.1. Minimum LP-Metric5.2. Marginality and Regularity5.3. Successful Coupling and Ergodicity5.4. Optimal Markovian Couplings5.5. Monotonicity5.6. Examples5.7. NotesPart Ⅱ. Symmetrizable Jump ProcessesChapter 6. Symmetrizable Jump Processes and Dirichlet Forms6.1. Reversible Markov Processes6.2. Existence6.3. Equivalence of Backward and Forward Kolmogorov Equations6.4. General Representation of Jump Processes6.5. Existence of Honest Reversible Jump Processes6.6. Uniqueness Criteria6.7. Basic Dirichlet Form6.8. Regularity, Extension and Uniqueness6.9. NotesChapter 7. Field Theory7.1. Field Theory7.2. Lattice Field7.3. Electric Field7.4. Transience of Symmetrizable Markov Chains7.5. Random Walk on Lattice Fractals7.6. A Comparison Theorem7.7. NotesChapter 8. Large Deviations8.1. Introduction to Large Deviations8.2. Rate Function8.3. Upper Estimates8.4. NotesChapter 9. Spectral Gap9.1. General Case: an Equivalence9.2. Coupling and Distance Method9.3. Birth-Death Processes9.4. Splitting Procedure and Existence Criterion9.5. Cheeger’’s Approach and Isoperimetric Constants9.6. NotesPart Ⅲ. Equilibrium Particle SystemsChapter 10. Random Fields10.1. Introduction10.2. Existence10.3. Uniqueness10.4. Phase Transition: Peierls Method10.5. Ising Model on Lattice Fractals10.6. Reflection Positivity and Phase Transitions10.7. Proof of the Chess-Board Estimates10.8. NotesChapter 11. Reversible Spin Processes and Exclusion Processes11.1. Potentiality for Some Speed Functions11.2. Constructions of Gibbs States11.3. Criteria for Reversibility11.4. NotesChapter 12. Yang-Mills Lattice Field12.1. Background12.2. Spin Processes from Yang-Mills Lattice Fields12.3. Diffusion Processes from Yang-Mills Lattice Fields12.4. NotesPart Ⅳ. Non-equilibrium Particle SystemsChapter 13. Constructions of the Processes13.1. Existence Theorems for the Processes13.2. Existence Theorem for Reaction-Diffusion Processes13.3. Uniqueness Theorems for the Processes13.4. Examples13.5. Appendix13.6. NotesChapter 14. Existence of Stationary Distributions and Ergodicity14.1. General Results14.2. Ergodicity for Polynomial Model14.3. Reversible Reaction-Diffusion Processes14.4. NotesChapter 15. Phase Transitions15.1. Duality15.2. Linear Growth Model15.3. Reaction-Diffusion Processes with Absorbing State15.4. Mean Field Method15.5. NotesChapter 16. Hydrodynamic Limits16.1. Introduction: Main Results16.2. Preliminaries16.3. Proof of Theorem 16.116.4. Proof of Theorem 16.316.5. NotesBibliographyAuthor IndexSubject Index