One-dimensional lattices topologically equivalent to two-dimensional lattices within the context of the lattice gas model

•Stochastics evolution equations.•Non-Markovian processes.•Lattice gas model.

Continuum partial differential equations are obtained from a set of discrete stochastic evolution equations of both non-Markovian and Markovian processes and applied to the diffusion within the context of the lattice gas model. A procedure allowing to construct one-dimensional lattices that are topologically equivalent to two-dimensional lattices is described in detail in the case of a rectangular lattice. This example shows the general features that possess the procedure and extensions are also suggested in order to provide a wider insight in the present approach.