Abstract
Active matter may sometimes behave almost indistinguishably from equilibrium matter. This is particularly evident for some particle-based models and active field-theories close to a critical point which falls in the Ising universality class. Here we show however that, even when critical, active particles strongly violate the equilibrium fluctuation-dissipation in the high-wave-vector and high-frequency regime. Conversely, at larger spatiotemporal scales the theorem is progressively restored and the critical dynamics is in effective equilibrium. We develop a field-theoretical description of this scenario employing a space-time correlated noise field finding that the theory qualitatively captures the numerical results already at the Gaussian level. Moreover a dynamic renormalization group analysis shows that the correlated noise does not change the equilibrium critical exponents. Our results demonstrate that a correlated noise field is a fundamental ingredient to describe critical active matter at the coarse-grained level.
Highlights
Active matter may sometimes behave almost indistinguishably from equilibrium matter
In this work we have studied numerically and analytically the dynamical properties of an active system around its Motility-Induced Phase Separation (MIPS) critical point
We have found that the Fluctuation Dissipation Theorem (FDT) is strongly violated at short time and length scales and that effective equilibrium is progressively restored at large spatiotemporal scales
Summary
Active matter may sometimes behave almost indistinguishably from equilibrium matter. This is evident for some particle-based models and active field-theories close to a critical point which falls in the Ising universality class. It has been pointed out that additional terms, which break the time reversal symmetry, could be included in the standard φ4 theory to capture the non-equilibrium and non-universal features near the MIPS critical point These terms turn out to be irrelevant from the point of view of Renormalization Group (RG) transformations, they might yield, for example, a non-zero entropy production rate[24]. Upon lowering the frequency and the wave-vector, we find that the response and correlator tend to coincide, satisfying FDT and validating the effective equilibrium picture To rationalize this numerical evidence, we put forward a colored-noise-driven dynamical field theory, that is able to explain the coarse-grained behavior of the active system. The overall picture, stemming from simulations and theory, unveils that a colored noise-field is a fundamental ingredient to describe near-critical active fluids
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