For a stochastic energy exchange model derived numerically from billiard dynamics, the paper proves a law of large numbers to a discrete heat equation, a central limit theorem, and an O(M^(-1)) approximation by a mesoscopic stochastic differential equation.
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From deterministic dynamics to thermodynamic laws II: Fourier's law and mesoscopic limit equation
For a stochastic energy exchange model derived numerically from billiard dynamics, the paper proves a law of large numbers to a discrete heat equation, a central limit theorem, and an O(M^(-1)) approximation by a mesoscopic stochastic differential equation.