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Introduction to Dynamic Transitions

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Phase Transition Dynamics

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Abstract

The study of phase transitions is an active field with a long history. This book aims to provide a comprehensive, unified, and balanced account of both dynamic and topological phase transition theories and their applications to statistical systems, quantum systems, classical and geophysical fluid dynamics, biological and chemical systems, and climate dynamics. The dynamic phase transition theory establishes a dynamic transition principle, Principle 1, following the philosophy of searching for a complete set of transition states. We present in this chapter a brief introduction to this dynamic transition theory together with an introduction to first-principle approach to fundamental laws of physics, and to fundamental issues of dynamic phase transitions motivated by problems in the nonlinear sciences.

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Notes

  1. 1.

    For brevity, we use here \(\lambda \in \mathbb R\).

  2. 2.

    See the beginning of Chap. 2 for the precise definition, and Ma and Wang (2005b) for more detailed discussions.

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Sichuan, China

    Tian Ma

  2. Department of Mathematics, Indiana University, Bloomington, IN, USA

    Shouhong Wang

Authors
  1. Tian Ma
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  2. Shouhong Wang
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Ma, T., Wang, S. (2019). Introduction to Dynamic Transitions. In: Phase Transition Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-030-29260-7_1

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