Field theories of active matter

Field theory has been one of the most successful methods for the characterisation of many-body systems for many decades. Different flavours of field theory, in particular the response-field formalism and Doi-Peliti field theory, have different advantages, with the latter maintaining particle entity by construction. The particulate nature of the degrees of freedom is of great importance to their entropy production and to active matter as a whole. In this presentation, I will briefly contrast the two approaches, before focussing on applications of Doi-Peliti field theory to active matter. Two of those are: 1) Calculating entropy production in active matter systems generally and 2) identifying the microscopic mechanism whereby repulsive pair-potentials become effectively attractive in the presence of self-propulsion, which underlies motility induced phase separation. Some food and some food for thought will be provided.