arXiv subjects

Oded Farago

Publications and source records attributed to Oded Farago.

At least 19 recordsLinked to original sources

arXiv2026

The Resetting Heat Engine: A Thermodynamic Cycle of Thermal Expansion and Compression

We consider a Brownian particle confined by an external potential and subject to stochastic resetting to the origin. Motivated by the repetitive nature of the dynamics, we describe the process as a thermodynamic cycle of thermal expansion and collapse, analyzed via a framework based on the Kullback-Leibler (KL) divergence between forward and reversed trajectory ensembles. While the entropy production generally depends on the full trajectory ensemble and cannot be reduced to thermodynamic state variables alone, we show that the harmonic potential constitute a special case, where the entropy production reduces exactly to a state-function-like expression determined solely by the distributions before and after resetting. Explicit analytical results are derived for periodic and Poissonian resetting. At low resetting rates $r$, the entropy production rate grows linearly with $r$ and is proportional to the symmetric KL divergence between the reset and equilibrium distributions. At very high rates, the resetting process becomes effectively perpetual and the entropy production vanishes. Langevin simulations for an anharmonic quartic potential display the same generic behavior, indicating that these features are not restricted to harmonic confinement. Our results establish a direct connection between stochastic resetting, thermodynamic cycles, and information-theoretic measures of irreversibility.

cond-mat.stat-mech↗

arXiv2025

Coupling of Lipid Phase Behavior and Protein Oligomerization in a Lattice Model of Raft Membranes

Membrane proteins often form dimers and higher-order oligomers whose stability and spatial organization depend sensitively on their lipid environment. To investigate the physical principles underlying this coupling, we employ a lattice Monte Carlo model of ternary lipid mixtures that exhibit liquid-disordered ($L_d$) and liquid-ordered ($L_o$) phase coexistence. In this framework, proteins are represented as small membrane inclusions with tunable nearest neighbor interactions with both lipids and other proteins, allowing us to examine how protein-lipid affinity competes with protein-protein interactions and lipid-lipid demixing. We find that the balance of these interactions controls whether proteins remain dispersed, assemble into small oligomers, or form large stable clusters within $L_o$ domains, and that increasing the protein concentration further promotes coarsening of the ordered phase. To incorporate ligand-regulated activation, we extend the model to a kinetic Monte Carlo scheme in which proteins stochastically switch between inactive and active states with distinct affinities. The inverse switching rate, relative to the time required for a protein to diffuse across the characteristic size of the $L_o$ domains, governs the aggregation behavior. Rapid switching yields only transient small oligomers, slow switching reproduces the static limit with persistent large clusters, and intermediate rates produce broad cluster-size distributions. These results highlight the interplay between lipid phase organization, protein-lipid affinity, and activation dynamics in regulating membrane protein oligomerization, a coupling that is central to signal transduction and membrane organization in living cells.

cond-mat.soft↗

arXiv2025

Inverse Clausius Thermodynamics in Run-and-Tumble Dynamics

We establish a mapping between one-dimensional run-and-tumble particle dynamics in the presence of thermal noise, and overdamped Brownian motion in a spatially inhomogeneous temperature field. The approach is formulated as an inverse-Clausius thermodynamic framework, where the effective temperature is inferred from the steady-state density. Within this mapping, the local entropy flux and entropy production rate can be extracted directly from steady-state observables, without requiring explicit knowledge of the full position-velocity distribution. The framework introduces a closure that, to leading order, relates entropy flow to spatial variations of effective temperature, yielding a picture of entropy transfer from hotter to colder regions. We apply the approach to two-state and multistate run-and-tumble models in harmonic and nonlinear potentials. For harmonic confinement, the closure is exact in the two-state case and very accurate in multistate models. For nonlinear potentials that are locally confining (positive curvature at the origin), comparable accuracy is observed. In contrast, potentials with vanishing or negative curvature require higher-order corrections and reveal a correspondence between the spatial structure of the entropy production rate and that of the confining potential.

cond-mat.stat-mech↗

arXiv2025

Steady state and relaxation dynamics of run and tumble particles in contact with a heat bath

We study the relaxation dynamics of a run and tumble particle in a one-dimensional piecewise linear potential $U(x)=b|x|$, from delta-function initial conditions at $x=0$ to steady state. In addition to experiencing active telegraphic noise, the particle is in contact with a heat bath at temperature $T$ that applies white thermal noise. We find that the position distribution of the RTP is described by a sum of two distributions ("modes"), each of which of the form $P(x,t\to\infty)\sim e^{-\lambda_i|x|}$ ($i=1,2$) at steady state. The two modes are dynamically coupled: At very short times ($t\to 0$), each mode stores half of the probability, and exhibits thermal diffusive spreading with a Gaussian profile. With progressing time and evolution toward steady state, the partition of probability between the modes becomes increasingly uneven and, depending on the model parameters, the mode with the smaller value of $\lambda_i$ may carry an overwhelming majority of the probability. Moreover, we identify that the characteristic relaxation time of each mode is $\tau_i=(\lambda_i^2T)^{-1}$, which implies that the minority mode also relaxes much faster than the dominant one. A more detailed analysis reveals that $\tau_i$ is characteristic of the mode relaxation only close to the origin at the core of the distribution, while further away it increases linearly with $|x|$ as if a relaxation front is propagating at constant speed $v_i^*=2\sqrt{T/\tau_i}$ in the system. The rate of non-equilibrium entropy production can be related to the two-mode splitting of the probability distribution and be expressed in terms of their correlation-lengths $\lambda_i$ and their contributions to the steady state distribution.

cond-mat.stat-mech↗

arXiv2025

Measuring the mechanical properties of asymmetric membranes in computer simulations -- new methods and insights

We present Monte Carlo simulations of an ultra coarse-grained lipid bilayer with different number of lipids on both leaflets. In the simulations, we employ a new method for measuring the elastic parameters of the membrane, including the area per lipid, area elasticity modulus, and bending rigidity. The method also allows to measure the spontaneous curvature and non-local bending modulus, which are not accessible by standard computer simulations with periodic boundary conditions. For membranes with lipid densities much smaller than the liquid to gel transition density, $\rho_g$, we find a very good agreement between the simulation results and the theory expressing the bilayer elastic free energy as the sum of quadratic free energies in the strains associated with the area density and the local curvature of the monolayers. The theory fails when the lipid area density (in the symmetric reference case) is only slightly smaller than $\rho_g$. Increasing the degree of asymmetry and changing the density of the condensed leaflet to a value larger than $\rho_g$, causes the layer to phase separate between regions with distinct densities which, in turn, may also induce density variations in the dilated liquid layer. Moreover, the phase separation may also trigger local curvature variations along the membrane, which can be attributed to the disparity between the values of the elastic parameters of the coexisting bilayer segments that are mechanically coupled. This mechanism leading to density-curvature variations and instabilities may play a role in cellular processes occurring in liquid-ordered raft domains that are surrounded by the disordered liquid matrix of the cell.

cond-mat.soft↗

arXiv2025

Realizing Quantitative Quasiparticle Modeling of Skyrmion Dynamics in Arbitrary Potentials

We demonstrate fully quantitative Thiele model simulations of magnetic skyrmion dynamics on previously unattainable experimentally relevant large length and time scales by ascertaining the key missing parameters needed to calibrate the experimental and simulation time scales and current-induced forces. Our work allows us to determine complete spatial pinning energy landscapes that enable quantification of experimental studies of diffusion in arbitrary potentials within the Lifson-Jackson framework. Our method enables us to ascertain the time scales, and by isolating the effect of ultra-low current density (order $10^6 A/m^2$) generated torques we directly infer the total force acting on the skyrmion for a quantitative modelling.

cond-mat.stat-mech↗

arXiv2024

Mixing small proteins with lipids and cholesterol

Many ternary mixtures composed of saturated and unsaturated lipids with cholesterol (Chol) exhibit a region of coexistence between liquid-disordered $(L_d)$ and liquid-ordered $(L_o)$ domains, bearing some similarities to lipid rafts in biological membranes. However, biological rafts also contain many proteins that interact with the lipids and modify the distribution of lipids. Here, we extend a previously published lattice model of ternary DPPC/DOPC/Chol mixtures by introducing a small amount of small proteins (peptides). We use Monte Carlo simulations to explore the mixing phase behavior of the components as a function of the interaction parameter representing the affinity between the proteins and the saturated DPPC chains, and for different mixture compositions. At moderate fractions of DPPC, the system is in a two-phase $L_d+L_o$ coexistence, and the proteins exhibit a simple partition behavior between the phases that depends on the protein-lipid affinity parameter. At low DPPC compositions, the mixture is in $L_d$ phase with local nanoscopic ordered domains. Addition of proteins with sufficiently strong attraction to the saturated lipids can induce the separation of a distinct $L_o$ large domain with tightly-packed gel-like clusters of proteins and saturated lipids. Consistent with the theory of phase transitions, we observe that the domain sizes grow when the mixture composition is in the vicinity of the critical point. Our simulations show that the addition of a small amount of proteins to such mixtures can cause their size to grow even further, and lead to the formation of metastable dynamic $L_o$ domains with sizes comparable to biological rafts.

cond-mat.soft↗

arXiv2024

Confined run and tumble particles with non-Markovian tumbling statistics

Confined active particles constitute simple, yet realistic, examples of systems that converge into a non-equilibrium steady state. We investigate a run-and-tumble particle in one spatial dimension, trapped by an external potential, with a given distribution $g(t)$ of waiting times between tumbling events whose mean value is equal to $τ$. Unless $g(t)$ is an exponential distribution (corresponding to a constant tumbling rate), the process is non-Markovian, which makes the analysis of the model particularly challenging. We use an analytical framework involving effective position-dependent tumbling rates, to develop a numerical method that yields the full steady-state distribution (SSD) of the particle's position. The method is very efficient and requires modest computing resources, including in the large-deviations and/or small-$τ$ regime, where the SSD can be related to the the large-deviation function, $s(x)$, via the scaling relation $P_{\rm st}(x)\sim e^{-s\left(x\right)/τ}$.

cond-mat.stat-mech↗

arXiv2023

Characterizing the heterogeneity of membrane liquid-ordered domains

We use a lattice model of a ternary mixture containing saturated and unsaturated lipids with cholesterol (Chol), to study the structural properties characterizing the coexistence between the liquid-disordered and liquid-ordered phases. Depending on the affinity of the saturated and unsaturated lipids, the system may exhibit macroscopic (thermodynamic) liquid-liquid phase separation, or be divided into small-size liquid-ordered domains surrounded by a liquid-disordered matrix. In both cases, it is found that the nano-scale structure of the liquid-ordered regions is heterogeneous, and that they are partitioned into Chol-rich sub-domains and Chol-free, gel-like, nano-clusters. This emerges as a characteristic feature of the liquid-ordered state, which helps distinguishing between liquid-ordered domains in a two-phase mixture, and similar-looking domains in a one-phase mixture that are rich in saturated lipids and Chol, but are merely thermal density fluctuations. The nano-structure heterogeneity of the liquid-ordered phase can be detected by suitable experimental spectroscopic methods, and is observed also in atomistic computer simulations.

cond-mat.soft↗

arXiv2023

A lattice model of ternary mixtures of lipids and cholesterol with tunable domain sizes

Much of our understanding of the physical properties of raft domains in biological membranes, and some insight into the mechanisms underlying their formation stem from atomistic simulations of simple model systems, especially ternary mixtures consisting of saturated and unsaturated lipids, and cholesterol (Chol). To explore the properties of such systems at large spatial scales, we here present a simple ternary mixture lattice model, involving a small number of nearest neighbor interaction terms. Monte Carlo simulations of mixtures with different compositions show an excellent agreement with experimental and atomistic simulation observations across multiple scale, ranging from the local distributions of lipids to the phase diagram of the system. The simplicity of the model allows us to identify the roles played by the different interactions between components, and the interplay between them. Importantly, by changing the value of one of the model parameters, we can tune the size of the liquid-ordered domains, thereby to simulate both Type II mixtures exhibiting macroscopic phase separation and Type I mixtures with nanoscopic domains. The Type II mixture simulation results fit well to the experimentally-determined phase diagram of mixtures containing saturated DPPC/unsaturated DOPC/Chol. When the tunable parameter is changed, we obtain the Type I version of DPPC/DOPC/Chol, i.e., a mixture not showing thermodynamic phase transitions but one that may be fitted to the same phase diagram if local measures are used to distinguish between the different states. Our model results suggest that short range packing is likely to be a key regulator of the stability and size distribution of biological rafts.

cond-mat.soft↗

arXiv2022

Nonequilibirum steady state for harmonically-confined active particles

We study the full nonequilibirum steady state distribution $P_{\text{st}}\left(X\right)$ of the position $X$ of a damped particle confined in a harmonic trapping potential and experiencing active noise, whose correlation time $τ_c$ is assumed to be very short. Typical fluctuations of $X$ are governed by a Boltzmann distribution with an effective temperature that is found by approximating the noise as white Gaussian thermal noise. However, large deviations of $X$ are described by a non-Boltzmann steady-state distribution. We find that, in the limit $τ_c \to 0$, they display the scaling behavior $P_{\text{st}}\left(X\right)\sim e^{-s\left(X\right)/τ_{c}}$, where $s\left(X\right)$ is the large-deviation function. We obtain an expression for $s\left(X\right)$ for a general active noise, and calculate it exactly for the particular case of telegraphic (dichotomous) noise.

cond-mat.stat-mech↗

arXiv2021

Minimal Lattice Model of Lipid Membranes with Liquid-Ordered Domains

Mixtures of lipids and cholesterol are commonly used as model systems for studying the formation of liquid-ordered ($L_o$) domains in heterogeneous biological membranes. The simplest model system exhibiting coexistence between $L_o$ domains and a liquid-disordered ($L_d$) matrix is that of a binary mixture of saturated lipids like DPPC and cholesterol (Chol). DPPC/Chol mixtures have been investigated for decades both experimentally, theoretically, and recently also by means of atomistic simulations. Here, we present a minimal lattice model that captures the correct behavior of this mixture across multiple scales. On the macroscopic scales, we present simulation results of mixtures of thousands of lipids and Chol molecules which show excellent agreement with the phase diagram of the system. The simulations are conducted on timescales of hundreds of microseconds and show the morphologies and dynamics of the domains. On the molecular scales, the simulations reveal local structures similar to those recently seen in atomistic simulations, including the formation of gel-like nano-domains ($\sim$ 1-10 nm) within larger Chol-rich $L_o$ domains ($\sim$ 10-100 nm). The observed multi-scale behavior is related to the tendency of Chol to induce ordering of acyl chains on the one hand, and disrupt their packing with each other, on the other hand.

cond-mat.soft↗

arXiv2021

Thermodynamics of a Brownian particle in a non-confining potential

We consider the overdamped Brownian dynamics of a particle starting inside a square potential well which, upon exiting the well, experiences a flat potential where it is free to diffuse. We calculate the particle's probability distribution function (PDF) at coordinate $x$ and time $t$, $P(x,t)$, by solving the corresponding Smoluchowski equation. The solution is expressed by a multipole expansion, with each term decaying $t^{1/2}$ faster than the previous one. At asymptotically large times, the PDF outside the well converges to the Gaussian PDF of a free Brownian particle. The average energy, which is proportional to the probability of finding the particle inside the well, diminishes as $E\sim 1/t^{1/2}$. Interestingly, we find that the free energy of the particle, $F$, approaches the free energy of a freely diffusing particle, $F_0$, as $δF=F-F_0\sim 1/t$, i.e., at a rate faster than $E$. We provide analytical and computational evidences that this scaling behavior of $δF$ is a general feature of Brownian dynamics in non-confining potential fields. Furthermore, we argue that $δF$ represents a diminishing entropic component which is localized in the region of the potential, and which diffuses away with the spreading particle without being transferred to the heat bath.

cond-mat.stat-mech↗

arXiv2020

Algorithms for Brownian dynamics across discontinuities

The problem of mass diffusion in layered systems has relevance to applications in different scientific disciplines, e.g., chemistry, material science, soil science, and biomedical engineering. The mathematical challenge in these type of model systems is to match the solutions of the time-dependent diffusion equation in each layer, such that the boundary conditions at the interfaces between them are satisfied. As the number of layers increases, the solutions may become increasingly complicated. Here, we describe an alternative computational approach to multi-layer diffusion problems, which is based on the description of the overdamped Brownian motion of particles via the underdamped Langevin equation. In this approach, the probability distribution function is computed from the statistics of an ensemble of independent single particle trajectories. To allow for simulations of Langevin dynamics in layered systems, the numerical integrator must be supplemented with algorithms for the transitions across the discontinuous interfaces. Algorithms for three common types of discontinuities are presented: (i) A discontinuity in the friction coefficient, (ii) a semi-permeable membrane, and (iii) a step-function chemical potential. The general case of an interface where all three discontinuities are present (Kedem-Katchalsky boundary) is also discussed. We demonstrate the validity and accuracy of the derived algorithms by considering a simple two-layer model system and comparing the Langevin dynamics statistics with analytical solutions and alternative computational results.

cond-mat.stat-mech↗

arXiv2020

A Langevin dynamics approach for multi-layer mass transfer problems

We use Langevin dynamics simulations to study the mass diffusion problem across two adjacent porous layers of different transport property. At the interface between the layers, we impose the Kedem-Katchalsky (KK) interfacial boundary condition that is well suited in a general situation. A detailed algorithm for the implementation of the KK interfacial condition in the Langevin dynamics framework is presented. As a case study, we consider a two-layer diffusion model of a drug-eluting stent. The simulation results are compared with those obtained from the solution of the corresponding continuum diffusion equation, and an excellent agreement is shown.

physics.comp-ph↗

arXiv2020

Defining velocities for accurate kinetic statistics in the GJF thermostat

We expand on two previous developments in the modeling of discrete-time Langevin systems. One is the well-documented Grønbech-Jensen Farago (GJF) thermostat, which has been demonstrated to give robust and accurate configurational sampling of the phase space. Another is the recent discovery that also kinetics can be accurately sampled for the GJF method. Through a complete investigation of all possible finite difference approximations to the velocity, we arrive at two main conclusions:~1) It is not possible to define a so-called on-site velocity such that kinetic temperature will be correct and independent of the time step, and~2) there exists a set of infinitely many possibilities for defining a two-point (leap-frog) velocity that measures kinetic energy correctly for linear systems in addition to the correct configurational statistics obtained from the GJF algorithm. We give explicit expressions for the possible definitions, and we incorporate these into convenient and practical algorithmic forms of the normal Verlet-type algorithms along with a set of suggested criteria for selecting a useful definition of velocity.

cond-mat.stat-mech↗

arXiv2020

'Rocket propulsion' of Janus micro-swimmers

We report simulations of a spherical Janus particle undergoing exothermic surface reactions around one pole only. Our model excludes self-phoretic transport by design. Nevertheless, net motion occurs from direct momentum transfer between solvent and colloid, with speed scaling as the square root of the energy released during the reaction. We find that such propulsion is dominated by the system's short-time response, when neither the time dependence of the flow around the colloid nor the solvent compressibility can be ignored. Our simulations agree reasonably well with previous experiments.

cond-mat.soft↗

arXiv2019

A simple statistical-mechanical interpretation of Onsager reciprocal relations and Derjaguin theory of thermo-osmosis

The application of a temperature gradient along a fluid-solid interface generates stresses in the fluid causing "thermo-osmotic" flow. Much of the understanding of this phenomenon is based on Derjaguin's work relating thermo-osmotic flows to the mechano-caloric effect, namely, the interfacial heat flow induced by a pressure gradient. This is done by using Onsager's reciprocity relationship for the equivalence of the thermo-osmotic and mechano-caloric cross-term transport coefficients. Both Derjaguin theory and Onsager framework for out-of-equilibrium systems are formulated in macroscopic thermodynamics terms and lack a clear interpretation at the molecular level. Here, we use statistical-mechanical tools to derive expressions for the transport cross-coefficients and, thereby, to directly demonstrate their equality. This is done for two basic models: (i) an incopressible continuum solvent containing non-interacting solute particles, and (ii) a single-component fluid without thermal expansivity. The derivation of the mechano-caloric coefficient appears to be remarkably simple, and provides a simple interpretation for the connection between interfacial heat and particle fluxes. We use this interpretation to consider yet another example, which is an electrolyte interacting with a uniformly-charged surface in the strong screening (Debye-Hückel) regime.

cond-mat.soft↗