A challenge of modern science has been to understand complex, highly correlated systems, from many-body problems in physics to living organisms in biology. Such systems are studied by all the classical sciences, and in fact the boundaries between scientific disciplines have been disappearing; ‘interdisciplinary’ has become synonymous with ‘timely’. Many general theoretical advances have been made, for instance the renormalization group theory of correlated many-body systems. However, in complex situations the value of analytical results obtained for simple, usually one-dimensional (1D) or effectively infinite-dimensional (mean-field), models has grown in importance. Indeed, exact and analytical calculations deepen understanding, provide a guide to the general behavior, and can be used to test the accuracy of numerical procedures.

A generation of physicists have enjoyed the book Mathematical Physics in One Dimension …, edited by Lieb and Mattis, which has recently been re-edited. But what about mathematical chemistry or mathematical biology in 1D? Since statistical mechanics plays a key role in complex, many-body systems, it is natural to use it to define topical coverage spanning diverse disciplines. Of course, there is already literature devoted to 1D models in selected fields, for instance, or to analytically tractable models in statistical mechanics, e.g.,. However, in recent years there has been a tremendous surge of research activity in 1D reactions, dynamics, diffusion, and adsorption. These developments are reviewed in this book.

There are several reasons for the flourishing of studies of 1D many-body systems with stochastic time evolution.