Additivity, density fluctuations, and nonequilibrium thermodynamics for active Brownian particles

Abstract

Using an additivity property, we study particle-number fluctuations in a system of interacting self-propelled particles, called active Brownian particles (ABPs), which consists of repulsive disks with random self-propulsion velocities. From a fluctuation-response relation -a direct consequence of additivity, we formulate a thermodynamic theory which captures the previously observed features of nonequilibrium phase transition in the ABPs from a homogeneous fluid phase to an inhomogeneous phase of coexisting gas and liquid. We substantiate the predictions of additivity by analytically calculating the subsystem particle-number distributions in the homogeneous fluid phase away from criticality where analytically obtained distributions are compatible with simulations in the ABPs.

Additivity and density fluctuations in Vicsek-like models of self-propelled particles

“…III C, we compare the number fluctuations in various self-propelled particle systems and that obtained from a hydrodynamic theory of Ref. [15]. Finally, in Sec.…”

“…1, see Ref. [15]. Now the equilibrium-like thermodynamic potentials µ(ρ) and f (ρ) can be readily calculated by integrating Eqs.…”

“…(10), (11) and (12) can be understood from that the Laplace transform of the weight factor W v (n) is related to the Legendre transform of the nonequilibrium free energy density function -an immediate consequence of additivity Eq. (1) [15]. Note that, through Eqs.…”

“…However, we note that, for higher noise strength (η ≥ 0.6) and large density, there are deviations from this particular scaling. Nevertheless, the To obtain a broader picture concerning the particlenumber fluctuations in the systems of self-propelled particles, in this section we compare the particle-number fluctuations in the Vicsek model, its variant and a system of active Brownian particles [5], which, unlike the Vicsek-like models, does not have any alignment interactions and was previously studied using additivity prop-erty [15]. Indeed, in the disordered isotropic phase, one would expect that, on the coarse-grained level, the presence of an alignment interaction would possibly change only the relaxation time scale of the polarization density field.…”

“…Moreover, the hydrodynamic theory, which was developed in the context of active Brownian particles in Ref. [15], could be then expected to capture fluctuations even in the Vicsek-like models with alignment interactions.…”