Reversible dynamics in discrete dissipative systems

The random walk model of Brownian motion is an example of a stochastic system which exhibits intrinsically irreversible behaviour. In spite of this, a simple discrete version of the model has been shown to harbour dynamics which are reversible and are described by a discrete form of Schrödingerʹs equation. The reversible dynamics appear as second order effects in this diffusive model, and the usual relationship between macroscopic irreversibility and microscopic reversibility is itself reversed. This will be discussed in the context of the `Brusselsʹ schoolʹ on irreversibility.