Current fluctuations of a self-interacting diffusion on a ring
arXiv:2406.15561 · doi:10.1088/1751-8121/ad9788
Abstract
We investigate fluctuations in the average speed or current of a self-interacting diffusion (SID) on a ring, mimicking the non-Markovian behaviour of an agent influenced by its own path. We derive the SID's phase diagram, showing a delocalisation-localisation phase transition from self-repelling to self-attracting. Current fluctuations are analysed using: (i) an adiabatic approximation, where the system reaches its stationary distribution before developing current fluctuations, and (ii) an original extension of level 2.5 large deviations for Markov processes combined with perturbation theory. Both methods provide lower bounds to current fluctuations, with the former tighter than the latter in all localised regimes, and both equally tight in the self-repelling region. Both methods accurately estimate the asymptotic variance and suggests a phase transition at the onset of the localised regime.
23 pages (18 + appendices and references), 4 figures. Accessible version at https://drive.google.com/file/d/1VjtzjSJvyPLZbDVKhS1US6-h-xk1X-Wu/view
References in corpus (30)
- The large deviation approach to statistical mechanics
- A survey of random processes with reinforcement
- Langevin Equation for the Density of a System of Interacting Langevin Processes
- Nonequilibrium Markov processes conditioned on large deviations
- Elephants can always remember: Exact long-range memory effects in a non-Markovian random walk
- Dynamic clustering and chemotactic collapse of self-phoretic active particles
- Amplitude Expansions for Instabilities in Populations of Globally-Coupled Oscillators
- Canonical structure of dynamical fluctuations in mesoscopic nonequilibrium steady states
- Collective Thermotaxis of Thermally Active Colloids
- Introduction to dynamical large deviations of Markov processes
- Distribution of Time-Averaged Observables for Weak Ergodicity Breaking
- Ergodicity and large deviations in physical systems with stochastic dynamics
- A formal view on 2.5 large deviations and fluctuation relations
- Current large deviations for driven periodic diffusions
- Chemotactic self-caging in active emulsions
- Effective dynamics of microorganisms that interact with their own trail
- Strong-coupling dynamics of a multi-cellular chemotactic system
- Collective Dynamics of Dividing Chemotactic Cells
- Current fluctuations in stochastic systems with long-range memory
- Dynamics of a microorganism moving by chemotaxis in its own secretion
- Large deviation function for the entropy production: Optimal trajectory and role of fluctuations
- Spatiotemporal Self-Organization of Fluctuating Bacterial Colonies
- Self Trapping of a Single Bacterium in its Own Chemoattractant
- On the diffusive-mean field limit for weakly interacting diffusions exhibiting phase transitions
- Giant leaps and long excursions: fluctuation mechanisms in systems with long-range memory
- Non-Equilibrium Thermodynamics and Topology of Currents
- Fluctuations in interacting particle systems with memory
- Trail-Mediated Self-Interaction
- Some particular self-interacting diffusions: Ergodic behaviour and almost sure convergence
- Long-term memory induced correction to Arrhenius law