Thermodynamics of Active Field Theories: Informatic vs Thermodynamic Entropy Production

The hallmark of active matter is the autonomous directed motion of its microscopic constituents driven by consumption of energy resources. This motion leads to the emergence of large-scale dynamics and structures without any equilibrium equivalent. Though active field theories offer a useful hydrodynamic description, it is unclear how to properly quantify the energetic cost of the dynamics from such a coarse-grained description. In this talk I will discuss a widely used measure of irreversibility we refer to as informatic entropy production and describe how it relates to the underlying energy dissipation or thermodynamic entropy production. Based on linear irreversible thermodynamics, we determine how active fields couple with the underlying reservoirs at the basis of nonequilibrium driving, which provide a thermodynamically consistent framework to identify the energy exchanges between active systems and their surrounding thermostat at the hydrodynamic level. This will be demonstrated in two popular active field theories: (i) the dynamics of a conserved density field reproducing active phase separation and (ii) the coupled dynamics of density and polarization describing motile deformable droplets.