The kinetic theory of gases has accomplished a sophisticated and hard task: to describe the response of a single physical system to a perturbation that pushed it away from its natural equilibrium state. This has been possible because the behavior of the projection to the \(\mu \) -space of the probability density in phase space (representing an ensemble of systems) can be identified with the behavior of the density of mass of a single system, under proper conditions. Apart from technicalities, it suffices that: 1. probability is transported in an exceedingly high dimensional very abstract phase space, as matter is transported in the concrete three-dimensional real space, and that 2. the Boltzmann-Grad limit, referring to rarefied gases, correctly represents the system of interest.

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Linear Response Theory

  • Carlos Mejía-Monasterio,
  • Lamberto Rondoni

摘要

The kinetic theory of gases has accomplished a sophisticated and hard task: to describe the response of a single physical system to a perturbation that pushed it away from its natural equilibrium state. This has been possible because the behavior of the projection to the \(\mu \) -space of the probability density in phase space (representing an ensemble of systems) can be identified with the behavior of the density of mass of a single system, under proper conditions. Apart from technicalities, it suffices that: 1. probability is transported in an exceedingly high dimensional very abstract phase space, as matter is transported in the concrete three-dimensional real space, and that 2. the Boltzmann-Grad limit, referring to rarefied gases, correctly represents the system of interest.