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328 results

Page 1 of 17

  • 4 - Linear Response Theory and Transport Phenomena

  • Roberto Livi, Università degli Studi di Firenze, Paolo Politi, Istituto dei Sistemi Complessi, Firenze
  • Book:
    Nonequilibrium Statistical Physics
    Published online:
    19 June 2025
    Print publication:
    03 July 2025, pp 141-197

  • Summary

    As a preliminary step toward linear response theory, the Kubo relation for the Brownian particle is described. The generalization of the fluctuation formalism to generalized thermodynamic observables is also illustrated, providing an explicit approach to linear response to external static, as well as time-dependent perturbation fields. Generalized fluctuation–dissipation relations are also introduced by this formalism. The Onsager regression relation is discussed as a basis for a general theory of transport processes, including coupled-transport phenomena.

  • 1 - Kinetic Theory and the Boltzmann Equation

  • Roberto Livi, Università degli Studi di Firenze, Paolo Politi, Istituto dei Sistemi Complessi, Firenze
  • Book:
    Nonequilibrium Statistical Physics
    Published online:
    19 June 2025
    Print publication:
    03 July 2025, pp 1-38
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  • Summary

    Kinetic theory is summarized as a mechanistic approach to thermodynamics, including the equilibrium state equation of an ideal gas and a phenomenological approach to its transport properties. The Boltzmann model of the ideal gas is described by the evolution equation of its distribution function in molecular space. The H-theorem is proved for both the uniform and nonuniform cases. The theorem of additive invariants allows to approach a fundamental formulation of hydrodynamic equations for both the ideal situation of an inviscid flow and for the more interesting case of a viscous flow.

  • 6 - Absorbing Phase Transitions

  • Roberto Livi, Università degli Studi di Firenze, Paolo Politi, Istituto dei Sistemi Complessi, Firenze
  • Book:
    Nonequilibrium Statistical Physics
    Published online:
    19 June 2025
    Print publication:
    03 July 2025, pp 242-270

  • Summary

    Absorbing phase transitions are an important class of nonequilibrium phase transitions. They are characterized by one or more absorbing states, defined as microscopic states from which the system cannot escape. The most famous case with one absorbing state is called directed percolation (a sort of driven version of the usual, isotropic percolation) and it represents, for example, the spreading of a disease through a contact process: If the infection rate is large enough with respect to the recovery rate, the asymptotic state shows a finite fraction of infected individuals. Models with one absorbing state, local dynamics, and no additional symmetries typically fall within the directed percolation universality class. We also provide a short introduction to self-organized criticality, devoting a section to the Bak–Tang–Wiesenfeld model.

Page 1 of 17