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Statistical Physics

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Interesting large scale behaviour can arise from short range local interactions between the constituent components of interacting particle systems.

This can manifest as long range correlations and dependencies, as well as more spectacular phenomena such as a phase transitions, where internal symmetries break down.

The study of probabilistic aspects of models of classical and quantum statistical physics involves many interesting topics, such as: phase transitions, fluctuations in the systems close to criticality or far from equilibrium, time dependent behaviour, diffusion in an environment that is spatially inhomogeneous but its statistical properties are translation invariant.

They can lead to extremely complex and difficult mathematics. To aid the study of these problems, we sometimes derive partial differential equations governing the macroscopic motion of the system from microscopic principles.