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2192 results in Statistical Physics

Page 3 of 110

  • 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

  • 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.

  • 5 - From Equilibrium to Out-of-Equilibrium Phase Transitions: Driven Lattice Gases

  • 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 198-241

  • Summary

    The first part of the chapter is a not-so-small presentation of equilibrium phase transitions, which allows us to introduce key concepts for both equilibrium and nonequilibrium phase transitions. The lattice gas, that is, the Ising model with a conserved order parameter, is an appropriate model to analyze how an equilibrium model can be brought out of equilibrium and to highlight the importance of boundary conditions in nonequilibrium phase transitions. The driven lattice gas, introduced by Katz, Lebowitz, and Spohn around 40 years ago, allows to define the totally asymmetric simple exclusion (TASEP) model and subsequently also the BRIDGE model. The latter is a one-dimensional model displaying a nonequilibrium phase transition with a symmetry breaking between two equivalent classes of particles. This result, considering the short-range character of interactions, would not be possible at equilibrium. In an equally unexpected way, an external breaking of the symmetry (equivalent to the application of a magnetic field to the Ising model) does not make the phase transition disappear.

Page 3 of 110