A comparison of dynamical fluctuations of biased diffusion and run-and-tumble dynamics in one dimension

Mallmin, Emil; Blythe, Richard A.; Evans, Martin R.

doi:10.1088/1751-8121/ab4349

Cited by 19 publications

(24 citation statements)

References 49 publications

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“…7 shows results for the rate function I(w) (Sec. II C), compared with the upper and lower bounds (39,43). We show data for lp = 5 as well as lp = 40, which was the case considered in [37].…”

Section: Numerical Evaluation Of Boundsmentioning

confidence: 99%

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Collective motion in large deviations of active particles

et al. 2021

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We analyse collective motion that occurs during rare (large deviation) events in systems of active particles, both numerically and analytically. We discuss the associated dynamical phase transition to collective motion, which occurs when the active work is biased towards larger values, and is associated with alignment of particles' orientations. A finite biasing field is needed to induce spontaneous symmetry breaking, even in large systems. Particle alignment is computed exactly for a system of two particles. For many-particle systems, we analyse the symmetry breaking by an optimal-control representation of the biased dynamics, and we propose a fluctuating hydrodynamic theory that captures the emergence of polar order in the biased state.

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Section: Numerical Evaluation Of Boundsmentioning

confidence: 99%

“…Several recent studies focused on large deviations of active matter [32][33][34][35][36][37][38][39][40][41][42]. They consider transient rare events where the system does not behave ergodically.…”

Section: Introduction a Motivationmentioning

confidence: 99%

Collective motion in large deviations of active particles

et al. 2021

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“…An important example of this singularityphase coexistence correspondence in equilibrium is the 2D Ising model below its critical temperature [1][2][3]8]. In dynamical models, singularities (kinks) of large-deviation functions develop in certain limits and can signal the emergence of a dynamical phase transition and the coexistence of distinct dynamical phases [9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Varied phenomenology of models displaying dynamical large-deviation singularities

Whitelam

Jacobson

2021

Phys. Rev. E

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Singularities of dynamical large-deviation functions are often interpreted as the signal of a dynamical phase transition and the coexistence of distinct dynamical phases, by analogy with the correspondence between singularities of free energies and equilibrium phase behavior. Here we study models of driven random walkers on a lattice. These models display large-deviation singularities in the limit of large lattice size, but the extent to which each model's phenomenology resembles a phase transition depends on the details of the driving. We also compare the behavior of ergodic and nonergodic models that present large-deviation singularities. We argue that dynamical large-deviation singularities indicate the divergence of a model timescale, but not necessarily one associated with cooperative behavior or the existence of distinct phases.

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“…The implications for the fluctuations of the active work is that the rate function, whose value controls the decay of the probability of atypical values of the active work with the observation time, grows linearly with the active work after a certain threshold. Such scenario is generally associated with a condensation-like transition at the level of fluctuations [59,60,61,62]: it would be of interest to understand whether a condensation mechanism is at work, possibly by extending our path-integral approach to the harmonically confined AOUP.…”

Section: Discussionmentioning

confidence: 99%

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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A comparison of dynamical fluctuations of biased diffusion and run-and-tumble dynamics in one dimension

Cited by 19 publications

References 49 publications

Collective motion in large deviations of active particles

Collective motion in large deviations of active particles

Varied phenomenology of models displaying dynamical large-deviation singularities

Work Fluctuations in the Active Ornstein- Uhlenbeck Particle model

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