Fluctuation-Dissipation Relations in the absence of Detailed Balance: formalism and applications to Active Matter

Cengio, Sara Dal; Levis, Demian; Pagonabarraga, Ignacio

doi:10.48550/arxiv.2007.07322

Cited by 8 publications

(8 citation statements)

References 84 publications

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“…Our aim is to determine to which extent one can obtain a fluctuation-dissipation relation (FDR) analogous to (99) for the active dynamics (1), a topic which has attracted interest recently [139][140][141]. These works are based on the explicit expression of the steady-state distribution of AOUPs.…”

Section: Effective Equilibrium: Linear Response and Fluctuation-dissi...mentioning

confidence: 99%

Statistical Mechanics of Active Ornstein Uhlenbeck Particles

Martin,

O'Byrne,

Cates

et al. 2020

Preprint

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We review and extend recent developments on the statistical properties of Active Ornstein Uhlenbeck particles (AOUPs). In this simplest of models, the Gaussian white noise of overdamped Brownian colloids is replaced by a Gaussian colored noise. This suffice to grant this system the hallmark properties of active matter, while still allowing for analytical progress. We first detail the perturbative derivation of the steady state of AOUPs in the small persistence time limit. We show the existence of an effective equilibrium regime in which detailed-balance is obeyed with respect to a non-Boltzmann distribution and detail the corresponding fluctuation-dissipation theorem. We then characterize the departure from equilibrium by computing several relevant observables (entropy production, ratchet current). At the collective level, we show AOUPs to experience motility-induced phase separation both in the presence of pairwise forces or due to quorum-sensing interactions. The latter can be accounted for by considering the steady-state of AOUPs with spatially varying propulsion speed or persistence time. Finally, we discuss how the emerging properties of AOUPs can be characterized from the dynamics of their collective modes, which we construct explicitly.

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Section: Effective Equilibrium: Linear Response and Fluctuation-dissi...mentioning

confidence: 99%

Statistical Mechanics of Active Ornstein Uhlenbeck Particles

Martin,

O'Byrne,

Cates

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…More general results holding also far from equilibrium, both for small and large activities, have been obtained after the generalization of the Malliavin weight sampling procedure to active particle dynamics [29]. For instance, this technique has been employed to numerically calculate i) the effective temperature of active systems [30][31][32][33][34], with a recent attention to phase-separation [35], and ii) the transport coefficients, such as the mobility, to test an approximated prediction valid at low-density values [36,37] iii) the response function due to a shear flow [38]. Finally, in recent studies based on path-integral approaches, generalized versions of the FDR holding also in far from equilibrium regimes have been reported in the specific case of athermal active particles [39,40].…”

Section: Introductionmentioning

confidence: 99%

Generalized Fluctuation-Dissipation relations holding in non-equilibrium dynamics

Caprini

2021

Preprint

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We derive generalized Fluctuation-Dissipation Relations (FDR) holding for a general stochastic dynamics that includes as subcases both equilibrium models for passive colloids and nonequilibrium models used to describe active particles. The relations reported here differ from previous formulations of the FDR because of their simplicity: they require only the microscopic knowledge of the dynamics instead of the whole expression of the steady-state probability distribution function that, except for linear interactions, is unknown for systems displaying non-vanishing currents. From the response function, we can extrapolate generalized versions of the Mesoscopic Virial equation and the equipartition theorem, which still holds far from equilibrium. Our results are tested in the case of equilibrium colloids described by underdamped or overdamped Langevin equations and for models describing the non-equilibrium behavior of active particles. Both the Active Brownian Particle and the Active Ornstein-Uhlenbeck particle models are compared in the case of a single particle confined in an external potential.

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“…Within the specific context of the AOUP model, it is interesting to notice the singularity of the harmonic case with respect to generic confining potentials. In this case, as in the free problem, the dynamics satisfies detailed balance [28,58], resulting in an effective equilibrium regime. As a result, the harmonically confined AOUP does not display the 'pushing' phase in steady state for any value of the parameters.…”

Section: Confined Active Ornstein-uhlenbeck Particlesmentioning

confidence: 97%

Work Fluctuations in the Active Ornstein- Uhlenbeck Particle model

Semeraro,

Suma,

Petrelli

et al. 2021

Preprint

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We study the large deviations of the power injected by the active force for an Active Ornstein-Uhlenbeck Particle (AOUP), free or in a confining potential. For the free-particle case, we compute the rate function analytically in d-dimensions from a saddle-point expansion, and numerically in two dimensions by a) direct sampling of the active work in numerical solutions of the AOUP equations and b) Legendre-Fenchel transform of the scaled cumulant generating function obtained via a cloning algorithm. The rate function presents asymptotically linear branches on both sides and it is independent of the system's dimensionality, apart from a multiplicative factor. For the confining potential case, we focus on two-dimensional systems and obtain the rate function numerically using both methods a) and b). We find a different scenario for harmonic and anharmonic potentials: in the former case, the phenomenology of fluctuations is analogous to that of a free particle, but the rate function might be non-analytic; in the latter case the rate functions are analytic, but fluctuations are realised by entirely different means, which rely strongly on the particle-potential interaction.

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Fluctuation-Dissipation Relations in the absence of Detailed Balance: formalism and applications to Active Matter

Cited by 8 publications

References 84 publications

Statistical Mechanics of Active Ornstein Uhlenbeck Particles

Statistical Mechanics of Active Ornstein Uhlenbeck Particles

Generalized Fluctuation-Dissipation relations holding in non-equilibrium dynamics

Work Fluctuations in the Active Ornstein- Uhlenbeck Particle model

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