Statistical Physics of Synchronization

1. Front Matter

   Pages i-xvi

   PDF

2. Synchronizing Systems

   • Shamik Gupta, Alessandro Campa, Stefano Ruffo

   Pages 1-38

3. Oscillators with First-Order Dynamics

   • Shamik Gupta, Alessandro Campa, Stefano Ruffo

   Pages 39-80

4. Oscillators with Second-Order Dynamics

   • Shamik Gupta, Alessandro Campa, Stefano Ruffo

   Pages 81-121

This book introduces and discusses the analysis of interacting many-body complex systems exhibiting spontaneous synchronization from the perspective of nonequilibrium statistical physics. While such systems have been mostly studied using dynamical system theory, the book underlines the usefulness of the statistical physics approach to obtain insightful results in a number of representative dynamical settings. Although it is intractable to follow the dynamics of a particular initial condition, statistical physics allows to derive exact analytical results in the limit of an infinite number of interacting units. Chapter one discusses dynamical characterization of individual units of synchronizing systems as well as of their interaction and summarizes the relevant tools of statistical physics. The latter are then used in chapters two and three to discuss respectively synchronizing systems with either a first- or a second-order evolution in time. This book provides a timely introduction to the subject and is meant for the uninitiated as well as for experienced researchers working in areas of nonlinear dynamics and chaos, statistical physics, and complex systems.

• spontaneous synchronization
• synchronizing systems
• Kuramoto model
• long-range interactions
• non-additive systems
• Fokker-Planck equation
• inequivalence of statistical ensembles
• breaking of ergodicity
• noisy synchronizing systems
• quenched random variables
• nonequilibrium steady states
• Mean-field analysis
• Limit-cycle oscillators
• Ott-Antonson solution
• Kramers equation
• complexity

• Department of Physics, Ramakrishna Mission Vivekananda University, Howrah, India

  Shamik Gupta

• National Center for Radiation Protection and Computational Physics, Istituto Superiore di Sanità, Roma, Italy

  Alessandro Campa

• SISSA, Trieste, Italy

  Stefano Ruffo

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