Manifestations of Projection-Induced Memory: General Theory and the Tilted Single File

Abstract

Over the years the field of non-Markovian stochastic processes and anomalous diffusion evolved from a specialized topic to mainstream theory, which transgressed the realms of physics to chemistry, biology and ecology. Numerous phenomenological approaches emerged, which can more or less successfully reproduce or account for experimental observations in condensed matter, biological and/or single-particle systems. However, as far as their predictions are concerned these approaches are not unique, often build on conceptually orthogonal ideas, and are typically employed on an ad hoc basis. It therefore seems timely and desirable to establish a systematic, mathematically unifying and clean approach starting from more fine-grained principles. Here we analyze projection-induced ergodic non-Markovian dynamics, both reversible as well as irreversible, using spectral theory. We investigate dynamical correlations between histories of projected and latent observables that give rise to memory in projected dynamics, and rigorously establish conditions under which projected dynamics is Markovian or renewal. A systematic metric is proposed for quantifying the degree of non-Markovianity. As a simple, illustrative but non-trivial example we study single file diffusion in a tilted box, which, for the first time, we solve exactly using the coordinate Bethe ansatz. Our results provide a solid foundation for a deeper and more systematic analysis of projection-induced non-Markovian dynamics and anomalous diffusion.

References in corpus (14)

• Anomalous transport in the crowded world of biological cells
• "Diffusing diffusivity": A model for anomalous and "anomalous yet Brownian" diffusion
• Anomalous diffusion: A basic mechanism for the evolution of inhomogeneous systems
• Diffusion-limited reactions in dynamic heterogeneous media
• Mean first-passage times of non-Markovian random walkers in confinement
• Single-File diffusion in a Box
• Non-ergodicity, fluctuations, and criticality in heterogeneous diffusion processes
• Collective dynamics effect transient subdiffusion of inert tracers in gel networks
• First passage time statistics for two-channel diffusion
• Localization and universal fluctuations in ultraslow diffusion processes
• Extreme value statistics of ergodic Markov processes from first passage times in the large deviation limit
• Anomalous fluctuations of currents in Sinai-type random chains with strongly correlated disorder
• Optimization and universality of Brownian search in quenched heterogeneous media
• Diffusion in periodic, correlated random forcing landscapes

Cited by in corpus (27)

• Faster uphill relaxation in thermodynamically equidistant temperature quenches
• Thermodynamic Uncertainty Relation Bounds the Extent of Anomalous Diffusion
• Spectral theory of fluctuations in time-average statistical mechanics of reversible and driven systems
• Violation of Local Detailed Balance Despite a Clear Time-Scale Separation
• Speedups in nonequilibrium thermal relaxation: Mpemba and related effects
• A Toolbox for Quantifying Memory in Dynamics Along Reaction Coordinates
• Single-file diffusion in a bi-stable potential: signatures of memory in the barrier-crossing of a tagged-particle
• Perspective: Time irreversibility in systems observed at coarse resolution
• Model-free inference of memory in conformational dynamics of a multi-domain protein
• On the emergence of memory in equilibrium versus non-equilibrium systems
• Asymmetric Thermal Relaxation in Driven Systems: Rotations go Opposite Ways
• Memory effects in colloidal motion under confinement and driving
• Dynamics of Micro and Nanoscale Systems in the Weak-Memory Regime
• Unified Linear Fluctuation-Response Theory Arbitrarily Far from Equilibrium
• Local time of an Ornstein-Uhlenbeck particle
• Nonequilibrium fluctuation-response relations for state-current correlations
• Nonequilibrium fluctuation-response relations for state observables
• BetheSF: Efficient computation of the exact tagged-particle propagator in single-file systems via the Bethe eigenspectrum
• Time- and ensemble-average statistical mechanics of the Gaussian Network Model
• Boundary conditions at a thin membrane that generate non--Markovian normal diffusion
• Macroscopic fluctuation-response theory and its use for gene regulatory networks
• The impact of memory on learning sequence-to-sequence tasks
• Dynamics of micro and nanoscale systems in the weak-memory regime: A mathematical framework beyond the Markov approximation
• Nonlinear Response Relations and Fluctuation-Response Inequalities for Nonequilibrium Stochastic Systems
• Purely quantum memory in closed systems observed via imperfect measurements
• Single file dynamics of tethered random walkers
• Weak-Memory Dynamics in Discrete Time