Non-equilibrium systems, which usually involve a large number of interacting particles, are ubiquitous in nature and society. Interactions, such as volume exclusion or branching, induce correlations in the system and often translate into emergent collec- tive behaviour at macroscopic scales. This is the case, for instance, in active matter, where particles are subject to local non-thermal forces that are transformed into mechanical work. Establishing the relationship between macroscopic patterns and microscopic dynamics analytically is a challenge that has motivated different approaches in the community.
In this thesis I have focused on some statistical properties with an emphasis on correlations, both spatial and temporal, of six different non-equilibrium particle systems: the Oslo rice pile model, branching processes and applications, the voter model, and run-and-tumble motion. The first three systems display critical phenomena and the last one is an instance of active motility.
The approaches that I have followed are, on the one hand, one-to-one mappings between different, known, stochastic processes and, on the other hand, the Doi-Peliti field theory formalism. The point in common between both approaches is the ability to retain the particle entity, which proves essential when tackling observables that strongly depend on the microscopic dynamics of the system, such as correlation functions. However, the field-theoretic approach is much more systematic, as it becomes apparent in the applicability of this route to different kinds of reaction-diffusion particle systems.Open Acces
