arXiv subjects

Roland R. Netz

Publications and source records attributed to Roland R. Netz.

At least 19 recordsLinked to original sources

arXiv2026

Reaction-Coordinate-Dependent Non-Markovian Friction Governs Protein-Folding Dynamics

It is common to project the full atomic-resolution representation of a protein onto a one-dimensionalreaction coordinate (RC) to capture the protein-folding kinetics. As a direct consequence ofthis dimensionality reduction, non-Markovian friction emerges in the framework of the general-ized Langevin equation (GLE). All previous applications of GLEs to protein folding employed anRC-independent friction memory function and therefore did not account for the different frictionin the folded and unfolded states. Using a recently derived GLE with RC-dependent mass andfriction memory function, we introduce a novel method to extract memory functions from timeseries data via a conditional Volterra equation. When applied to molecular dynamics (MD) data ofsix fast-folding proteins, we find strongly RC-dependent memory friction in line with the intuitiveexpectation that friction is higher in the folded than in the unfolded state due to internal proteinfriction. Our numerically efficient method to simulate the GLE confirms the accuracy of the GLEparameter extraction by comparison with the MD data. We show that RC-dependent memoryfriction not only adds physical insight into the folding process but also significantly improves thedescription of protein folding kinetics using low-dimensional RCs.

physics.bio-ph↗

arXiv2026

Comparison of different exact generalized Langevin equations with a non-linear potential of mean force and an observable-dependent mass and friction

The Mori-Zwanzig projection formalism constitutes a powerful and robust framework for deriving equations of motion in terms of generalized Langevin equations (GLEs) for an arbitrary observable using evolution and projection operators. Based on this framework, we analyze the properties of four distinct GLEs for a scalar observable including a Markovian force derived from a generally non-linear potential, a non-Markovian friction force, and an orthogonal force, commonly interpreted as a random force. While all four GLEs are exact, they differ in the memory friction kernel, which may either be dependent or independent of the observable, and by the potential, which may either include or exclude the effective kinetic energy of the observable. Inclusion of the kinetic energy in the potential is advantageous for observables whose velocity satisfies Wick's theorem, since this reproduces the correct distribution of the observable and its velocity even without contributions from the friction force and the orthogonal force.

cond-mat.stat-mech↗

arXiv2026

Microscopic Structure and Dynamics of Interfacial Water at Fluorinated vs Nonfluorinated Surfaces -- Insights from Ab-Initio Simulations and IR Spectroscopy

Per- and polyfluoroalkyl substances are a class of synthetic chemical compounds widely used as coatings to lower surface energies. Yet the microscopic mechanisms of their weak interaction with water and organic compounds remain poorly understood. Here, we perform large-scale density-functional-theory molecular dynamics simulations to investigate water at self-assembled monolayers (SAMs) of fluorinated and non-fluorinated hydrocarbons. We analyze the interfacial water structure and compare it to the prototypical hydrophobic air-water interface. The interfacial water structure at both SAMs closely resembles that at the air-water interface, featuring a distinct depletion layer and a two-dimensional hydrogen-bond network parallel to the surface. Computed anisotropic infrared spectra reproduce key experimental signatures observed in surface-enhanced infrared absorption spectroscopy (SEIRAS), including the presence of free OH vibrations directly probing the local surface-water interactions. Notably, while the free OH stretch at the hydrocarbon SAM-water interface exhibits a red shift relative to the air-water interface, indicative of weak binding, the fluorinated SAM-water interface displays a weakly blue-shifted free OH mode, in agreement with experiment. This frequency behavior defies common interpretations based on the vibrational Stark effect. Further, we show that the reorientation dynamics of water molecules are significantly slower near the fluorinated surface, which we correlate with spectral line shapes, an effect rather expected at hydrophilic surfaces. This indicates that fluorinated SAMs, despite being macroscopically more hydrophobic than their unfluorinated counterparts, exhibit spectroscopic characteristics that neither qualify it as hydrophobic nor hydrophilic.

physics.chem-ph↗

arXiv2026

Complementary Eigen-Zundel Interpretation Reconciles Thermodynamics and Spectroscopy of Excess Protons in Aqueous HF Solutions

Aqueous solutions of HF and HCl behave very differently at intermediate concentrations: HCl dissociates completely, whereas HF remains only partially dissociated and forms bifluoride (HF$_2^-$). This should lead to different excess-proton spectra in HF and HCl solutions, in contrast to experimental reports. Using ab initio molecular dynamics, we show that in HF the proton is not firmly bound to F$^-$, as suggested by textbook chemistry, but dynamically shared with a hydrating water molecule. This is rationalized by a modified Eigen-state description which also explains the formation of HF$_2^-$. The similar vibrational spectra of HF and HCl solutions are explained by a complementary Zundel picture in terms of almost identical excess proton transfer free-energy profiles for HF and HCl. These results reconcile thermodynamic and spectroscopic observations and provide a unified microscopic picture of excess protons in aqueous solution.

physics.chem-ph↗

arXiv2026

Non-equilibrium generalized Langevin equation for multi-dimensional observables

The Mori-Zwanzig formalism is a powerful theoretical framework for deriving equations of motion for coarse-grained observables in the form of generalized Langevin equations (GLEs) involving evolution and projection operators. Using a time-dependent many-body Hamiltonian and a multi-dimensional Mori projection operator, we derive a non-equilibrium Mori GLE for a multi-dimensional observable of interest $\vec{A}$ that consists of a Markovian force, a running integral over time of a non-Markovian friction force, and an orthogonal force that is often interpreted as a random force. We study the structure of the derived GLE in three limiting cases: when the components of $\vec{A}$ are uncorrelated, when the Hamiltonian is time-independent and thus the system is at equilibrium, and when both conditions are simultaneously satisfied. We highlight the presence of a contribution to the Markovian force that takes the form of an instantaneous friction force which only vanishes when the components of $\vec{A}$ are uncorrelated. Our non-Markovian framework is an important step towards the systematic modeling of the coupled kinetics of coarse-grained reaction coordinates in biological complex systems, exemplified for the coupled intra- and inter-protein folding during fibril formation of the human islet amyloid polypeptide (IAPP).

cond-mat.stat-mech↗

arXiv2026

Non-Markovian non-equilibrium modeling of experimental cell-motion trajectories reveals dependence of propulsion-force correlations on solvent viscosity

Cell motility underlies many biological processes, including cancer metastasis, bacterial infection, and evolutionary adaptation. We introduce a non-equilibrium single-cell motility model inspired by the generalized Langevin equation, which accounts for hydrodynamic friction and correlated propulsion force. From video microscopy of Chlamydomonas reinhardtii algae and Salmonella typhimurium bacteria we extract the propulsion-force dynamics on the single-cell level, which we find to exhibit multi-exponential correlations, not captured by literature non-equilibrium cell-motility models. Based on our data-driven model, we predict the effective cell diffusivities beyond experimentally resolved timescales and demonstrate a diffusivity maximum at intermediate solvent viscosity for both cell types. This means that cells adapt their propulsion-force characteristics according to the solvent viscosity. In addition, our model predicts the power output of single cells, which is on the order of aW for the salmonella and fW for the algae.

physics.bio-ph↗

arXiv2026

Beyond the Electric Dipole Approximation: Electric and Magnetic Multipole Contributions Reveal Biaxial Water Structure from SFG Spectra at the Air-Water Interface

The interpretation of sum-frequency-generation (SFG) spectra has been severely limited by the absence of quantitative theoretical predictions of higher-order multipole contributions. Magnetic dipole and electric quadrupole contributions are determined by bulk properties but appear in all experimental SFG spectra, obscuring the connection between measured spectra and interfacial structure. We present the simulation-based framework to predict the full set of multipole spectral contributions. This framework also yields depth-resolved spectra, enabling the precise spatial localization of spectroscopic features. Applied to the air-water interface, our approach achieves quantitative agreement with experimental spectra for different polarization combinations in both the bending and stretching regions. Higher-order multipole contributions are crucial for correctly interpreting SFG spectra: in the bending band, the electric dipole and the magnetic dipole contributions have similar intensities, while the electric quadrupole contribution is significantly larger. In the OH-stretch region, the electric quadrupole contribution is found to be in large part responsible for the characteristic shoulder at 3600/cm. Crucially, subtracting the quadrupole and magnetic contributions isolates the second-order electric dipole susceptibility, which is a quantitative probe for interfacial molecular orientational anisotropy. This electric-dipole susceptibility reveals a pronounced biaxial ordering of water at the air-water interface. By resolving a fundamental limitation of the interpretation of SFG spectroscopy, our framework allows for the detailed extraction of interfacial water ordering from SFG spectra.

cond-mat.stat-mech↗

arXiv2026

Barrier-crossing and energy relaxation dynamics of non-Markovian inertial systems connected via analytical Green-Fokker-Planck approach

From numerical simulations it is known that the barrier-crossing time of a non-Markovian one-dimensional reaction coordinate with a single exponentially decaying memory function exhibits a memory-turnover: for intermediate values of the memory decay time the barrier-crossing time is reduced compared to the Markovian limit and for long memory times increases quadratically with the memory time when keeping the total integrated friction and the mass constant. The intermediate memory acceleration regime is accurately predicted by Grote-Hynes theory, for the asymptotic long-memory slow-down behavior no systematic analytically tractable theory is available. Starting from the Green function for a general inertial (i.e. finite-mass) non-Markovian Gaussian reaction coordinate in a harmonic well, we derive by an exact mapping a generalized Fokker-Planck equation with a time-dependent effective diffusion constant. To first order in a systematic cumulant expansion we derive an analytical Arrhenius expression for the barrier-crossing time with the pre-exponential factor given by the energy relaxation time, which can be used to robustly predict barrier-crossing times from simulation or experimental trajectory data of general non-Markovian inertial systems without the need to extract memory functions. For a single exponential memory kernel we give a closed-form expression for the barrier-crossing time, which reproduces the Kramers turnover between the high-friction and high-mass limits as well as the memory turnover from the intermediate memory acceleration to the asymptotic long-memory slow-down regime. We also show that non-Markovian systems are singular in the zero-mass limit, which suggests that the long-memory barrier-crossing slow-down reflects the interplay between mass and memory effects. Thus, physically sound models for non-Markovian systems have to include a finite mass.

cond-mat.stat-mech↗

arXiv2026

Combined effects of evaporation, sedimentation and solute crystallization on the dynamics of aerosol size distributions on multiple length and time scales

We investigate three aspects of aerosol-mediated air-borne viral infection mechanisms on different length and time scales. First, we address the evolution of the size distribution of a non-interacting ensemble of droplets that are subject to evaporation and sedimentation using a sharp droplet-air interface model. From the exact solution of the evolution equation we derive the viral load in the air and show that it depends sensitively on the relative humidity. Secondly, from Molecular Dynamics simulations we extract the molecular reflection coefficient of single water molecules from the air-water interface. This parameter determines the water condensation and evaporation rate at a liquid droplet surface and therefore the evaporation rate of aqueous droplets. We find the reflection of water to be negligible at room temperature but to rise significantly at elevated temperatures and for grazing incidence angles. Thirdly, we derive a thermodynamically consistent three-dimensional diffuse-interface model for solute-containing droplets that is formulated as a three-phase Cahn-Hilliard/Allen-Cahn system. By numerically solving the coupled system of equations, we explore representative scenarios that show that this model reproduces and generalizes features of the sharp-interface model. These interconnected studies on the dynamics of aerosol droplet evaporation are relevant in order to quantitatively assess the airborne infection risk under varying environmental conditions.

physics.flu-dyn↗

arXiv2025

Static Dielectric Permittivity Profiles and Coarse-graining Approaches for Water in Graphene Slit Pores

The dielectric response of nano-confined fluids is crucial across technologies and biological systems, yet its calculation and interpretation from molecular simulations are often muddled by unclear boundary conditions. We re-derive the Green--Kubo relation for the spatially resolved linear dielectric response of fluids in planar confinement, explicitly accounting for boundary conditions and showing that equilibrium-derived profiles agree with those obtained from external fields. We identify common misconceptions in the literature and outline how microscopic dielectric behavior can be coarse-grained to connect with experimental observables. Simulations show that water retains a bulk-like dielectric response down to $\sim 1\,\mathrm{nm}$ confinement. The reduced \emph{effective} dielectric response that governs capacitance arises from the placement of the dielectric interface. Using effective-medium theory, we demonstrate that long-range reductions reported in experiments and theory are consistent with bulk-like behavior beyond about $1\,\mathrm{nm}$ from the surface. The effective response naturally maps onto an interfacial capacitance, and the dielectric properties of simulated water are robust across simulation setups and water models, reflecting universal polarization correlations.

cond-mat.soft↗

arXiv2025

Sub-Nanometer Interfacial Hydrodynamics: The Interplay of Interfacial Viscosity and Surface Friction

For an accurate description of nanofluidic systems, it is crucial to account for the transport properties of liquids at surfaces on sub-nanometer scales, where classical hydrodynamics fails due to the finite range of surface-liquid interactions and modifications of the local viscosity. We show how to account for both via generalized, position-dependent surface-friction and interfacial viscosity profiles, which enables the accurate description of interfacial flow on the nanoscale using the Stokes equation. Such profiles are extracted from non-equilibrium molecular dynamics simulations of water on polar, non-polar, fluorinated, and unfluorinated alkane and alcohol self-assembled monolayers of widely varying wetting characteristics. Power-law relationships among the Navier friction coefficient, interfacial viscosity excess, and depletion length are revealed, and these are each found to be exponential in the work of adhesion. Our framework forms the basis for describing sub-nanometer fluid flow at interfaces with implications for electrokinetics, biophysics, and nanofluidics.

cond-mat.soft↗

arXiv2025

Hierarchical friction memory leads to subdiffusive configurational dynamics of fast-folding proteins

Proteins often exhibit subdiffusive configurational dynamics. The origins of this subdiffusion are still unresolved. We investigate the impact of non-Markovian friction and the free energy landscape on the dynamics of fast-folding proteins in terms of the mean squared displacement (MSD) and the mean first-passage-time (MFPT) of the folding reaction coordinate. We find the friction memory kernel from published molecular dynamics (MD) simulations to be well-described by a hierarchical multi-exponential function, which gives rise to subdiffusion in the MSD over a finite range of time. We show that friction memory effects in fast-folding proteins dominate the scaling behavior of the MSD compared to effects due to the folding free energy landscape. As a consequence, Markovian models are insufficient for capturing the folding dynamics, as quantified by the MSD and the MFPT, even when including coordinate-dependent friction. Our results demonstrate the importance of memory effects in protein folding and conformational dynamics and explicitly show that subdiffusion in fast-folding protein dynamics originates from memory effects, not from the free energy landscape and not from coordinate-dependent friction.

cond-mat.soft↗

arXiv2025

The influence of multi-dimensionality and off-diagonal non-Markovian friction coupling on coarse-grained dynamics

Coarse-graining complex molecular systems to lower-dimensional reaction coordinates is a powerful approach for capturing their effective dynamics. The generalized Langevin equation (GLE) provides an exact framework for modeling coarse-grained dynamics, and is particularly useful when non-Markovian effects are significant. While one-dimensional GLE models are commonly used, many systems require multi-dimensional reaction coordinates to account for coupled dynamics. Here, we study the GLE formalism for multi-dimensional reaction coordinates, incorporating a memory matrix to quantify non-Markovian frictional coupling between coordinates, and a multi-dimensional potential. Using the GLE model, in conjunction with a multi-dimensional Markovian embedding scheme, we investigate different systems that are characterized by two-dimensional reaction coordinates, namely the dihedral dynamics of pentane and alanine dipeptide, obtained from molecular dynamics simulations in explicit water. We identify significant off-diagonal friction couplings arising from intramolecular and hydrodynamic interactions. Unlike previous studies, our results highlight the critical role of different terms in the multi-dimensional GLE in accurately capturing key dynamical properties, including mean first-passage times and mean-squared displacements, particularly in systems with coupled non-Markovian coordinates.

physics.chem-ph↗

arXiv2025

Subdiffusion from competition between multi-exponential friction memory and energy barriers

Subdiffusion is a hallmark of complex systems, ranging from protein folding to transport in viscoelastic media. However, despite its pervasiveness, the mechanistic origins of subdiffusion remain contested. Here, we analyze both Markovian and non-Markovian dynamics, in the presence and absence of energy barriers, in order to disentangle the distinct contributions of memory-dependent friction and energy barriers to the emergence of subdiffusive behavior. Focusing on the mean squared displacement (MSD), we develop an analytical framework that connects subdiffusion to multiscale memory effects in the generalized Langevin equation (GLE), and derive the subdiffusive scaling behavior of the MSD for systems governed by multi-exponential memory kernels. We identify persistence and relaxation timescales that delineate dynamical regimes in which subdiffusion arises from either memory or energy barrier effects. By comparing analytical predictions with simulations, we confirm that memory dominates the overdamped dynamics for barrier heights up to approximately $2\,k_BT$, a regime recently shown to be relevant for protein folding. Overall, our results advance the theoretical understanding of anomalous diffusion and provide practical tools that are broadly applicable to fields as diverse as molecular biophysics, polymer physics, and active matter systems.

cond-mat.soft↗

arXiv2025

Analysis and Simulation of Generalized Langevin Equations with Non-Gaussian Orthogonal Forces

The generalized Langevin equation (GLE) is a useful framework for analyzing and modeling the dynamics of many-body systems in terms of low-dimensional reaction coordinates, with its specific form determined by the choice of projection formalism. We compare parameters derived from different GLE formulations using molecular dynamics simulations of butane's dihedral angle dynamics. Our analysis reveals non-Gaussian contributions of the orthogonal force in different GLEs, being most enhanced for the Mori-GLE, where all non-linearities are relegated to the orthogonal force. We establish a simulation technique that correctly accounts for non-Gaussian orthogonal forces, which is critical for accurately predicting dihedral-angle mean first-passage times. We find that the accuracy of GLE simulations depends significantly on the chosen GLE formalism; the Mori-GLE offers the most numerically robust framework for capturing the statistical observables of the dihedral angle dynamics, provided the correct non-Gaussian orthogonal force distribution is used.

physics.comp-ph↗

arXiv2025

The Importance of Layer-Dependent Molecular Twisting for the Structural Anisotropy of Interfacial Water

The unique structural properties of interfacial water are at the heart of a vast range of important processes in electrochemistry, climate science, and biophysics. At interfaces, water molecules exhibit preferential orientations and an altered intermolecular H-bond connectivity. Characterising this layer-dependent anisotropic structure for such a thin molecular boundary, however, is a veritable challenge, with many important details remaining unknown. Here, we combine a novel depth-resolved second-order spectroscopy with molecular dynamics simulations to study the anisotropic structure at the air-water interface through the H-O-H bending vibration. We firstly show that the experimental nonlinear spectrum contains a large bulk like (quadrupolar) contribution that has hampered the assessment of the interfacial structure in previous investigations. By subtracting this contribution, we uncover the elusive anisotropic interfacial response that quantitatively matches the simulated prediction. Thereafter, by analysing both the vibrational line-shape of the interfacial spectrum and its depth-dependence, we demonstrate that both the molecular tilt and twist angles of water must be highly restricted at the interface, which is confirmed by the simulated orientational distribution. Finally, by analysing the depth and orientation dependence of the bending frequency, we show substantial deviations from the expected behaviour, revealing an anomalous character to the interfacial H-bond network.

physics.chem-ph↗

arXiv2025

Nonlocal dielectric properties of water: the role of electronic delocalisation

The nonlocal dielectric properties of liquid water are studied in the context of {\it ab initio} molecular dynamics simulations based on density functional theory. We calculate the dielectric response from the charge structure factor of the liquid using the fluctuation-dissipation theorem. We show that the dielectric response function of {\it ab initio} simulations differs significantly from that of classical force-fields, both qualitatively and quantitatively. In particular, it exhibits a larger amplitude and a wider range of responding wave numbers. We suggest that the difference is due to the localisation of the electronic charge density inherent in classical force files and Wannier post-treatment of DFT densities. The localised charge models do not reproduce the shape of the response function even for $q$ corresponding to intermolecular distances, and could lead to a significant underestimation of the dielectric response of the liquid by a factor of 10.

physics.chem-ph↗

arXiv2025

Dielectric properties of aqueous electrolytes at the nanoscale

Despite the ubiquity of aqueous electrolytes, the effect of salt on water organization remains controversial. We introduce a nonlocal and nonlinear field theory for the nanoscale polarization of ions and water and derive the electrolyte dielectric response as a function of salt concentration to first order in a loop expansion. By comparison with molecular dynamics simulations, we show that rising salt concentration induces a dielectric permittivity decrement and Debye screening in the longitudinal susceptibility but leaves the water structure remarkably unchanged.

cond-mat.soft↗