The book "Phase Transition Dynamics" by Tian Ma and Shouhong Wang provides a comprehensive and unified dynamic transition theory for dissipative systems, with applications to a wide range of problems in the nonlinear sciences. The authors classify dynamic transitions into three categories: continuous, catastrophic, and random, extending the classical classification of equilibrium phase transitions. The book aims to derive a general principle for dynamic transitions, establish a systematic theory, and explore its physical implications. Key topics include: - **Introduction to Dynamic Transitions**: Discusses the principles, models, and classifications of dynamic transitions. - **Dynamic Transition Theory**: Provides a detailed mathematical framework, including the classification of transitions, local topological structures, and the structure of transition states. - **Equilibrium Phase Transition in Statistical Physics**: Examines equilibrium phase transitions in systems like PVT, ferromagnetism, binary systems, superconductivity, and superfluidity. - **Fluid Dynamics**: Analyzes transitions in classical fluid dynamics, such as Rayleigh–Bénard convection, Taylor–Couette flow, and rotating convection. - **Geophysical Fluid Dynamics and Climate Dynamics**: Studies transitions in geophysical flows, including El Niño–Southern Oscillation, thermohaline ocean circulation, and atmospheric circulations. - **Dynamical Transitions in Chemistry and Biology**: Focuses on transitions in chemical reactions (Belousov–Zhabotinsky) and biological systems (chemotaxis and population models). The book is designed for graduate students and researchers in mathematics, physics, and related fields, providing both theoretical insights and practical applications.The book "Phase Transition Dynamics" by Tian Ma and Shouhong Wang provides a comprehensive and unified dynamic transition theory for dissipative systems, with applications to a wide range of problems in the nonlinear sciences. The authors classify dynamic transitions into three categories: continuous, catastrophic, and random, extending the classical classification of equilibrium phase transitions. The book aims to derive a general principle for dynamic transitions, establish a systematic theory, and explore its physical implications. Key topics include: - **Introduction to Dynamic Transitions**: Discusses the principles, models, and classifications of dynamic transitions. - **Dynamic Transition Theory**: Provides a detailed mathematical framework, including the classification of transitions, local topological structures, and the structure of transition states. - **Equilibrium Phase Transition in Statistical Physics**: Examines equilibrium phase transitions in systems like PVT, ferromagnetism, binary systems, superconductivity, and superfluidity. - **Fluid Dynamics**: Analyzes transitions in classical fluid dynamics, such as Rayleigh–Bénard convection, Taylor–Couette flow, and rotating convection. - **Geophysical Fluid Dynamics and Climate Dynamics**: Studies transitions in geophysical flows, including El Niño–Southern Oscillation, thermohaline ocean circulation, and atmospheric circulations. - **Dynamical Transitions in Chemistry and Biology**: Focuses on transitions in chemical reactions (Belousov–Zhabotinsky) and biological systems (chemotaxis and population models). The book is designed for graduate students and researchers in mathematics, physics, and related fields, providing both theoretical insights and practical applications.