Lack of an equation of state for the nonequilibrium chemical potential of gases of active particles in contact

Abstract

We discuss the notion of nonequilibrium chemical potential in gases of non-interacting active particles filling two compartments separated by a potential energy barrier. Different types of active particles are considered: run-and-tumble particles, active Brownian particles, and active Brownian particles with a stochastic reorientation along an external field. After recalling some analytical results for run-and-rumble particles in one dimension, we focus on the two-dimensional case and obtain a perturbative expression of the density profile in the limit of a fast reorientation dynamics, for the three models of active particles mentioned above. Computing the chemical potentials of the non-equilibrium systems in contact from the knowledge of the stationary probability distribution of the whole system -which agrees with a recently proposed general definition of the chemical potential in non-equilibrium systems in contact-we generically find that the chemical potential lacks an equation of state, in the sense that it depends on the detailed shape of the potential energy barrier separating the compartments and not only on bulk properties, at odds with equilibrium. This situation is reminiscent of the properties of the mechanical pressure in active systems. We also argue that the Maxwell relation is no longer valid and cannot be used to infer the nonequilibrium chemical potential from the knowledge of the mechanical pressure.

Phase coexistence of active Brownian particles

“…Connections to work in driven lattice systems [54], in particular on phase coexistence far from equilibrium [55,56], and to the more general case of interacting dissipative units [57] are worth exploring. It would also be interesting to investigate the effects of adding further external forces, such as those due to ramp-like external potentials considered in [22,58]. As the force balance without such a perturbation is already a delicate one, we expect profound changes upon such alterations, possibly similar to the changes that occur to equilibrium phase separation in confinement by external fields.…”

Aggregate morphology of active Brownian particles on porous, circular walls

“…Although MIPS is a highly nonequilibrium process, its qualitative similarities to equilibrium liquid-gas phase separation have motivated the formulation of an effective thermodynamic approach to explaining this phenomenon. Such descriptions involve formulations of pressure [18][19][20][21][22][23][24][25][26][27], surface tension [28][29][30][31], and chemical potential [32][33][34], in the context of active systems.…”

Non-additive large deviations function for the particle densities of driven systems in contact

“…, and recalling that ρ A = ρ A + ∆N A /V A , one gets at leading order in V A the macroscopic detailed balance (21).…”

“…Such an approach actually relies on a additivity property of the large deviations function describing density fluctuations in subsystems [15,16,17,18,19]. Recent works have more explicitly focused on the properties of the non-equilibrium chemical potential, which turns out to generically depend on the contact dynamics and to lack an equation of state [20,21,22]. The validity of the additivity condition has been traced back to both a macroscopic detailed balance condition at contact and a factorization of the contact dynamics [20,22].…”