arXiv subjects

Jae-Hyung Jeon

Publications and source records attributed to Jae-Hyung Jeon.

At least 19 recordsLinked to original sources

arXiv2026

Ornstein-Uhlenbeck Process Driven by Multiple Dichotomous Noises

We study a generalized Ornstein-Uhlenbeck process driven by a superposition of $K$ independent dichotomous noises with arbitrary fixed amplitudes and switching rates. Unlike the classical Ornstein-Uhlenbeck process driven by equilibrium Gaussian white noise, the present system is governed by bounded nonequilibrium fluctuations with finite correlation times. We obtain exact expressions for the stationary position distribution and all cumulants, and show that the stationary state possesses an unexpectedly rich structure, including compact support, algebraic branch-point singularities, edge divergences, and multiple extrema. We establish a mapping onto a heterogeneous random-flight process with bounded jumps, yielding a transparent probabilistic interpretation of the stationary measure. We further analyze several limiting regimes, including the crossover to Gaussian statistics for large numbers of noise sources. For ensembles with exponentially-distributed quenched amplitudes, we derive exact disorder-averaged stationary distributions and show that disorder fundamentally alters the stationary state, producing exponential tails decorated by algebraic prefactors with non-trivial exponents.

cond-mat.stat-mech↗

arXiv2026

Power spectral density of trajectories of active Ornstein-Uhlenbeck particles

The power spectral density (PSD) is a central frequency-domain descriptor of stochastic processes. While PSDs have been studied for Brownian motion and a few anomalous diffusion processes, the spectral densities of active nonequilibrium processes remain almost unexplored. Here, we present an exact theory for the PSDs of active diffusion using the model of active Ornstein-Uhlenbeck particles (AOUPs). We investigate the spectral densities of AOUPs in free space and under harmonic confinement. In free space, active motion does not alter the Brownian $f^{-2}$ spectrum, but only modifies its amplitude and introduces a crossover at the persistence frequency. Under confinement, the spectrum exhibits a rich variety of features depending on the persistence, trap relaxation, and activity strength, including two characteristic signatures that are absent in both thermal systems and free AOUPs. These are a two-plateau structure from a double-trapping mechanism due to two noise sources, and the new $f^{-4}$ spectral scaling associated with transient ballistic motion. We also investigate the finite time effects through the finite-time PSD, and find that the low-frequency plateau and high frequency oscillation exhibit distinct dependences on the observation time $T$ in free and confined systems. Finally, we discuss our results in connection with previously reported experimental studies of active systems. Our results provide an analytically tractable framework for interpreting such systems.

cond-mat.stat-mech↗

arXiv2026

Anomalous statistics in the Langevin equation with fluctuating diffusivity: from Brownian yet non-Gaussian diffusion to anomalous diffusion and ergodicity breaking

Diffusive motion is a fundamental transport mechanism in physical and biological systems, governing dynamics across a wide range of scales -- from molecular transport to animal foraging. In many complex systems, however, diffusion deviates from classical Brownian behaviour, exhibiting striking phenomena such as Brownian yet non-Gaussian diffusion (BYNGD) and anomalous diffusion. BYNGD describes a frequently observed statistical feature characterised by the coexistence of linear mean-square displacement (MSD) and non-Gaussian displacement distributions. Anomalous diffusion, in contrast, involves a nonlinear time dependence of the MSD and often reflects mechanisms such as trapping, viscoelasticity, heterogeneity, or active processes. Both phenomena challenge the conventional framework based on constant diffusivity and Gaussian statistics. This review focuses the theoretical modelling of such behaviour via the Langevin equation with fluctuating diffusivity (LEFD) -- a flexible stochastic framework that captures essential features of diffusion in heterogeneous media. LEFD not only accounts for BYNGD but also naturally encompasses a wide range of anomalous transport phenomena, including subdiffusion, ageing, and weak ergodicity breaking. Ergodicity is discussed in terms of the correspondence between time and ensemble averages, as well as the trajectory-to-trajectory variability of time-averaged observables. The review further highlights the empirical relevance of LEFD and related models in explaining diverse experimental observations and underscores their value to uncovering the physical mechanisms governing transport in complex systems.

cond-mat.stat-mech↗

arXiv2026

Diffusing diffusivity model with dichotomous noise

We study Langevin dynamics with stochastic diffusivity arising from fluctuations of the surrounding medium. The diffusivity is modeled as Ornstein-Uhlenbeck process driven by symmetric dichotomous noise, which confines it to a finite interval. We derive analytical expressions for the short-time probability density function (PDF) of the particle displacement and analyse its asymptotic behaviour. While the PDF retains the characteristic logarithmic divergence at the origin, its tails differ from the Gaussian white-noise case: exponential tails are replaced by Gaussian ones modulated by a power-law with a switching-rate-dependent exponent. At long times, the dynamics converges to ordinary Gaussian diffusion. We determine the variance and covariance of the time-averaged stochastic diffusivity and show that it is self-averaging. The model provides a minimal analytically tractable framework for stochastic transport in environments with bounded or switching fluctuations.

cond-mat.stat-mech↗

arXiv2026

Anomalous diffusion in coupled viscoelastic media: A fractional Langevin equation approach

Anomalous diffusion often arises in complex environments where viscoelastic or crowded conditions influence particle motion. In many biological and soft-matter systems, distinct components of the medium exhibit unique viscoelastic responses, resulting in time-dependent changes in the observed diffusion exponents. Here, we develop a theoretical model of two particles, each embedded in a distinct viscoelastic medium, and coupled via a harmonic potential. By formulating and solving a system of coupled fractional Langevin equations (FLEs) with memory exponents $0<α<β\leq 1$, we uncover rich transient anomalous diffusion phenomena arising from the interplay of memory kernels and bilinear coupling. Notably, we identify recovery dynamics, where a subdiffusive particle ($α$) transiently accelerates and eventually regains its intrinsic long-time mobility. This recovery emerges only when memory exponents differ ($α<β$), whereas identical exponents ($α=β$) suppress recovery. Our theoretical predictions offer insight into experimentally observed transient anomalous diffusions, such as polymer--protein complexes and cross-linked cytoskeletal networks, highlighting the critical role of memory heterogeneity and mechanical interactions in biological anomalous diffusion.

cond-mat.soft↗

arXiv2025

Single-Trajectory Bayesian Modeling Reveals Multi-State Diffusion of the MSH Sliding Clamp

DNA mismatch repair (MMR) is the essential mechanism for preserving genomic integrity in various living organisms. In this process, MutS homologs (MSH) play crucial roles in identifying mismatched basepairs and recruiting downstream MMR proteins. The MSH protein exhibits distinct functions and diffusion dynamics before and after the recognition of mismatches while traversing along DNA. An ADP-bound MSH, known as the MSH searching clamp, scans DNA sequences via rotational diffusion along the DNA backbone. Upon recognizing a mismatch, the MSH combines with ATP molecules, forming a stable sliding clamp. Recent experimental evidence challenges the conventional view that the sliding clamp performs a simple Brownian motion. In this study, we explore the diffusion dynamics of the ATP-bound MSH sliding clamp through single-particle tracking experiments and introduce a Bayesian single-trajectory modeling framework to analyze its motion. Our quantitative analysis reveals that the diffusion characteristics defy explanation by a single-state diffusion mechanism. Instead, our in-depth model inference uncovers three distinct diffusion states, each characterized by specific diffusion coefficients. These states alternate over time, with cross-state transitions predominantly involving one intermediate state, and direct transitions between the slowest and the fastest states being scarce. We propose that these multi-state dynamics reflect underlying conformational changes in the MSH sliding clamp, highlighting a more intricate diffusion mechanism than previously appreciated.

physics.bio-ph↗

arXiv2025

Objective comparison of methods to decode anomalous diffusion

Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The characterization of anomalous diffusion from the measurement of an individual trajectory is a challenging task, which traditionally relies on calculating the trajectory mean squared displacement. However, this approach breaks down for cases of practical interest, e.g., short or noisy trajectories, heterogeneous behaviour, or non-ergodic processes. Recently, several new approaches have been proposed, mostly building on the ongoing machine-learning revolution. To perform an objective comparison of methods, we gathered the community and organized an open competition, the Anomalous Diffusion challenge (AnDi). Participating teams applied their algorithms to a commonly-defined dataset including diverse conditions. Although no single method performed best across all scenarios, machine-learning-based approaches achieved superior performance for all tasks. The discussion of the challenge results provides practical advice for users and a benchmark for developers.

physics.data-an↗

arXiv2025

Thermodynamic uncertainty relation for systems with active Ornstein-Uhlenbeck particles

Thermodynamic uncertainty relations (TURs) delineate tradeoff relations between the thermodynamic cost and the magnitude of an observable's fluctuation. While TURs have been established for various nonequilibrium systems, their applicability to systems influenced by active noise remains largely unexplored. Here, we present an explicit expression of TUR for systems with active Ornstein-Uhlenbeck particles (AOUPs). Our findings reveal that active noise introduces modifications to the terms associated with the thermodynamic cost in the TUR expression. The altered thermodynamic cost encompasses not only the conventional entropy production but also the energy consumption induced by the active noise. We examine the capability of this TUR as an accurate estimator of the extent of anomalous diffusion in systems with active noise driven by a constant force in free space. By introducing the concept of a contracted probability density function, we derive a steady-state TUR tailored to this system. Moreover, through the adoption of a new scaling parameter, we enhance and optimize the TUR bound further. Our results demonstrate that active noise tends to hinder accurate estimation of the anomalous diffusion extent. Our study offers a systematic approach for exploring the fluctuation nature of biological systems operating in active environments.

cond-mat.stat-mech↗

arXiv2025

Fickian yet non-Gaussian diffusion in an annealed heterogeneous environment

Fickian yet non-Gaussian diffusion is a ubiquitous phenomenon observed in various biological and soft matter systems. This anomalous dynamics is typically attributed to heterogeneous environments inducing spatiotemporal variations in the diffusivity of tracer particles. While previous studies have predominantly focused on systems exhibiting either spatial or temporal heterogeneity, this work bridges the gap by introducing a model based on an annealed extreme landscape to simultaneously account for both types of heterogeneities. Through a combination of computational analyses and analytical derivations, we investigate how the interplay of spatial and temporal heterogeneities in the energy landscape gives rise to Fickian yet non-Gaussian diffusion. Furthermore, we demonstrate that in the presence of temporal environmental fluctuations, the heterogeneous diffusion inevitably converges to classical Brownian motion via a homogenization process. We derive an analytical expression for the homogenization time as a function of key parameters governing the system's spatiotemporal heterogeneities. Additionally, we quantify particle-to-particle diffusion heterogeneity and examine the ergodic properties of this model, providing deeper insights into the dynamics of complex, heterogeneous systems.

cond-mat.stat-mech↗

arXiv2024

Generalized Langevin equation for a tagged monomer in a Gaussian semiflexible polymer

In this study, we present a comprehensive analysis of the motion of a tagged monomer within a Gaussian semiflexible polymer model. We carefully derived the generalized Langevin Equation (GLE) that governs the motion of a tagged central monomer. This derivation involves integrating out all the other degrees of freedom within the polymer chain, thereby yielding an effective description of the viscoelastic motion of the tagged monomer. A critical component of our analysis is the memory kernel that appears in the GLE. By examining this kernel, we characterized the impact of bending rigidity on the non-Markovian diffusion dynamics of the tagged monomer. Furthermore, we calculated the mean-squared displacement of the tagged monomer using the derived GLE. Our results not only show remarkable agreement with previously known results in certain limiting cases but also provide dynamic features over the entire timescale.

cond-mat.soft↗

arXiv2024

Exploring the Interplay of Intrinsic Fluctuation and Complexity in Intracellular Calcium Dynamics

The concentration of intracellular calcium ion (Ca$^{2+}$) exhibits complex oscillations, including bursting and chaos, as observed experimentally. These dynamics are influenced by inherent fluctuations within cells, which serve as crucial determinants in cellular decision-making processes and fate determination. In this study, we systematically explore the interplay between intrinsic fluctuation and the complexity of intracellular cytosolic Ca$^{2+}$ dynamics using complexity measures such as permutation entropy (PE) and statistical complexity (SC). Using the chemical Langevin equation, we simulate the stochastic dynamics of cytosolic Ca$^{2+}$. Our findings reveal that PE and SC effectively characterize the diverse, dynamic states of cytosolic Ca$^{2+}$ and illustrate their interactions with intrinsic fluctuation. PE analysis elucidates that the chaotic state is more sensitive to intrinsic fluctuation than the other periodic states. Furthermore, we identify distinct states of cytosolic Ca$^{2+}$ occupying specific locations within the theoretical bounds of the complexity-entropy causality plane. These locations indicate varying complexity and information content as intrinsic fluctuation varies. When adjusting the permutation order, the SC for the different states exhibits peaks in an intermediate range of intrinsic fluctuation values. Additionally, we identify scale-free or self-similar patterns in this intermediate range, which are further corroborated by multifractal detrended fluctuation analysis. These high-complexity states likely correspond to optimal Ca$^{2+}$ dynamics with biological significance, revealing rich and complex dynamics shaped by the interplay of intrinsic fluctuation and complexity. Our investigation enhances our understanding of how intrinsic fluctuation modulates the complexity of intracellular Ca$^{2+}$ dynamics that play crucial roles in biological cells.

nlin.AO↗

arXiv2024

Active Diffusion of Self-Propelled Particles in Semi-Flexible Polymer Networks

Mesh-like structures, such as mucus gel or cytoskeleton networks, are ubiquitous in biological systems. These intricate structures are composed of cross-linked, semi-flexible bio-filaments, crucial to numerous biological processes. In many biological systems, active self-propelled particles like motor proteins or bacteria navigate these intricate polymer networks. In this study, we develop a computational model of three-dimensional cubic-topological, swollen polymer networks of semi-flexible filaments. We perform Langevin dynamics simulations to investigate the diffusion of active tracer particles navigating through these networks. By analyzing various physical observables, we investigate the effects of mesh-to-particle size ratio, Péclet number of active particles, and bending stiffness of the polymer networks upon active trapped-and-hopping diffusion of the tracer. When the tracer size is equal to or larger than the mesh size, the polymer stiffness substantially enhances trapping while suppressing the hopping process. Notably, the mean trapped time exhibits an exponential growth law to the bending stiffness with an activity-dependent slope. An analytic theory based on the mean first-passage time of active particles in a harmonic potential is developed. Our findings deepen the comprehension of the intricate interplay between the polymer's bending stiffness, tracer size, and the activity of tracer particles. This knowledge can shed light on important biological processes, such as motor-driven cargo transport or drug delivery, which hinge on the behavior of active particles within biological gels.

cond-mat.soft↗

arXiv2023

Viscoelastic active diffusion governed by nonequilibrium fractional Langevin equations: underdamped dynamics and ergodicity breaking

In this work, we investigate the active dynamics and ergodicity breaking of a nonequilibrium fractional Langevin equation (FLE) with a power-law memory kernel of the form $K(t)\sim t^{-(2-2H)}$, where $1/2<H<1$ represents the Hurst exponent. The system is subjected to two distinct noises: a thermal noise satisfying the fluctuation-dissipation theorem and an active noise characterized by an active Ornstein-Uhlenbeck process with a propulsion memory time $τ_\mathrm{A}$. We provide analytic solutions for the underdamped active fractional Langevin equation, performing both analytical and computational investigations of dynamic observables such as velocity autocorrelation, the two-time position correlation, ensemble- and time-averaged mean-squared displacements (MSDs), and ergodicity-breaking parameters. Our results reveal that the interplay between the active noise and long-time viscoelastic memory effect leads to unusual and complex nonequilibrium dynamics in the active FLE systems. Furthermore, the active FLE displays a new type of discrepancy between ensemble- and time-averaged observables. The active component of the system exhibits ultraweak ergodicity breaking where both ensemble- and time-averaged MSDs have the same functional form with unequal amplitudes. However, the combined dynamics of the active and thermal components of the active FLE system are eventually ergodic in the infinite-time limit. Intriguingly, the system has a long-standing ergodicity-breaking state before recovering the ergodicity. This apparent ergodicity-breaking state becomes exceptionally long-lived as $H\to1$, making it difficult to observe ergodicity within practical measurement times. Our findings provide insight into related problems, such as the transport dynamics for self-propelled particles in crowded or polymeric media.

cond-mat.stat-mech↗

arXiv2023

Nonequilibrium diffusion of active particles bound to a semi-flexible polymer network: simulations and fractional Langevin equation

In a viscoelastic environment, the diffusion of a particle becomes non-Markovian due to the memory effect. An open question is to quantitatively explain how self-propulsion particles with directional memory diffuse in such a medium. Based on simulations and analytic theory, we address this issue with active viscoelastic systems where an active particle is connected with multiple semi-flexible filaments. Our Langevin dynamics simulations show that the active cross-linker displays super- and sub-diffusive athermal motion with a time-dependent anomalous exponent $α$. In such viscoelastic feedback, the active particle always has superdiffusion with $α=3/2$ at times shorter than the self-propulsion time ($τ_A$). At times greater than $τ_A$, the subdiffusion emerges with $α$ bounded between $1/2$ and $3/4$. Remarkably, the active subdiffusion is reinforced as the active propulsion (Pe) is more vigorous. In the high-Pe limit, the athermal fluctuation in the stiff filament eventually leads to $α=1/2$, which can be misinterpreted with the thermal Rouse motion in a flexible chain. We demonstrate that the motion of active particles cross-linking a network of semi-flexible filaments can be governed by a fractional Langevin equation combined with fractional Gaussian noise and an Ornstein-Uhlenbeck noise. We analytically derive the velocity autocorrelation function and mean-squared displacement of the model, explaining their scaling relations as well as the prefactors. We find that there exist the threshold Pe ($\mathrm{Pe}^*$) and cross-over times ($τ^*$ and $τ^\dagger$) above which the active viscoelastic dynamics emerge on the timescales of $τ^* \lesssim t \lesssim τ^\dagger$. Our study may provide a theoretical insight into various nonequilibrium active dynamics in intracellular viscoelastic environments.

cond-mat.soft↗

arXiv2022

Accessing power-law statistics under experimental constraints

Over the last decades, impressive progresses have been made in many experimental domains, e.g. microscopic techniques such as single-particle tracking, leading to plethoric amounts of data. In a large variety of systems, from natural to socio-economic, the analysis of these experimental data conducted us to conclude about the omnipresence of power-laws. For example, in living systems, we are used to observing anomalous diffusion, e.g. in the motion of proteins within the cell. However, estimating the power-law exponents is challenging. Both technical constraints and experimental limitations affect the statistics of observed data. Here, we investigate in detail the influence of two essential constraints in the experiment, namely, the temporal-spatial resolution and the time-window of the experiment. We study how the observed distribution of an observable is modified by them and analytically derive the expression of the power-law distribution for the observed distribution through the scope of the experiment. We also apply our results on data from an experimental study of the transport of mRNA-protein complexes along dendrites.

cond-mat.stat-mech↗

arXiv2022

Bayesian inference of scaled versus fractional Brownian motion

We present a Bayesian inference scheme for scaled Brownian motion, and investigate its performance on synthetic data for parameter estimation and model selection in a combined inference with fractional Brownian motion. We include the possibility of measurement noise in both models. We find that for trajectories of a few hundred time points the procedure is able to resolve well the true model and parameters. Using the prior of the synthetic data generation process also for the inference, the approach is optimal based on decision theory. We include a comparison with inference using a prior different from the data generating one.

stat.ME↗

arXiv2022

Active diffusion of self-propelled particles in flexible polymer networks

Biopolymer networks having a meshwork topology, e.g., extracellular matrix and mucus gels, are ubiquitous. It is an open question to understand how self-propelled agents such as Janus colloidal particles diffuse through such a biopolymer network. Here, we computationally explore this issue in-depth by explicitly modeling three-dimensional biopolymer networks and performing Langevin dynamics simulations of active diffusion of the self-propelled tracers therein. We show that the active tracer performs distinct diffusion dynamics depending on the mesh-to-particle size and Péclet number (Pe). When the particle is smaller than the mesh size, it moves as if in free space with a decreased mobility depending on the polymer occupation density and Pe. However, when the particle size is increased to be comparable to the mesh size, the active particles explore the polymer network using the trapped-and-hopping mechanism. We study the trapped time distribution, flight length distribution, the mean-squared displacement, and the long-time diffusivity at varying Pe. If the particle is larger than the mesh, it captures the collective viscoelastic dynamics from the polymer network at short times and the simple diffusion of the total system at large times. Finally, we discuss the scaling behavior of the long-time diffusivity with Pe, where we find a range of Pe that yields a nontrivial power law. The latter turns out to arise from a large fluctuation of trapped, activated tracers in conjugation with responsive polymer networks.

cond-mat.soft↗

arXiv2021

Fractal and knot-free chromosomes facilitate nucleoplasmic transport

Chromosomes in the nucleus assemble into hierarchies of 3D domains that, during interphase, share essential features with a knot-free condensed polymer known as the fractal globule (FG). The FG-like chromosome likely affects macromolecular transport, yet its characteristics remain poorly understood. Using computer simulations and scaling analysis, we show that the 3D folding and macromolecular size of the chromosomes determine their transport characteristics. Large-scale subdiffusion occurs at a critical particle size where the network of accessible volumes is critically connected. Condensed chromosomes have connectivity networks akin to simple Bernoulli bond percolation clusters, regardless of the polymer models. However, even if the network structures are similar, the tracer's walk dimension varies. It turns out that the walk dimension depends on the network topology of the accessible volume and dynamic heterogeneity of the tracer's hopping rate. We find that the FG structure has a smaller walk dimension than other random geometries, suggesting that the FG-like chromosome structure accelerates macromolecular diffusion and target-search.

physics.bio-ph↗