Field Theory of stochastic particle systems

Field theory has been a major work-horse of statistical mechanics for a long time, because it naturally accommodates many interacting agents within the same framework and is easily extended to incorporate additional interactions and reactions. A particularly interesting application is active matter, where particles turn environmental energy, i.e. chemical fuel, into mechanical energy, for example self-propulsion. Doi-Peliti field theories are designed to retain the particle nature of the constituents of such stochastic particle systems. In the present talk, I will review how Doi-Peliti field theories can be built and used to characterise active matter to reveal how it breaks time-reversal symmetry.

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