Thermodynamics of active field theories: Energetic cost of coupling to reservoirs

TL;DR

This paper develops a thermodynamically consistent framework to quantify the energetic cost of active matter systems at the hydrodynamic level, linking heat dissipation to nonequilibrium activity and irreversibility.

Contribution

It introduces a novel approach to measure heat dissipation in active field theories, connecting microscopic energy exchanges to coarse-grained hydrodynamic descriptions.

Findings

Spatial maps of heat dissipation reveal regions of high energetic cost.

Dissipated heat correlates with the degree of order in active systems.

The framework applies to models of phase separation and motile droplets.

Abstract

The hallmark of active matter is the autonomous directed motion of its microscopic constituents driven by consumption of energy resources. This 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. We provide a thermodynamically consistent framework to identify the energy exchanges between active systems and their surrounding thermostat at the hydrodynamic level. Based on linear irreversible thermodynamics, we determine how active fields couple with the underlying reservoirs at the basis of nonequilibrium driving. This leads to evaluating the rate of heat dissipated in the thermostat, as a measure of the cost to sustain the system away from equilibrium, which is related to the irreversibility of the active field dynamics. We demonstrate the applicability of our approach 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. Combining numerical and analytical approaches, we provide spatial maps of dissipated heat, compare them with the irreversibility measure of the active field dynamics, and explore how the overall dissipated heat varies with the emerging order.