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An Isaac Newton Institute Programme

Principles of the Dynamics of Non-Equilibrium Systems

Chaos and the physics of non-equilibrium systems

18th April 2006

Author: H van Beijeren (Utrecht)


After a brief introduction to chaos theory I will summarize some of the methods for relating it to non-equilibrium statistical mechanics.Then I will show how to use kinetic theory methods to calculate characteristic chaotic properties such as Lyapunov exponents and Kolmogorov-Sinai entropies for dilute interacting particle systems. For the Lorentz gas (a system of light point particles moving among fixed scatterers) these calculations are especially simple, but they can also be done for systems of moving hard spheres. Finally, I will consider the case of the Brownian motion of one large sphere in a very dilute gas of small spheres. Under these conditions the largest Lyapunov exponents are due to the Brownian particle. They can be calculated by solving a Fokker-Planck equation.