arXiv subjects

Dmitrii E. Makarov

Publications and source records attributed to Dmitrii E. Makarov.

15 recordsLinked to original sources

arXiv2026

Modern view of activated rate processes: unidirectional fluxes at equilibrium, correlation functions, and splitting probabilities

More than 80 years ago Kramers published a paper calculating how fast a Brownian particle escapes from a potential well over an activation barrier. Since then Kramers' model has been widely adopted by nuclear physics, biophysics and chemical physics communities as a description of activated barrier crossing. From a chemical kinetics perspective, Kramers' theory provides a mapping from continuous dynamics to discrete-state chemical kinetics. Motivated by recent developments, this Perspective provides a rigorous way of performing such a mapping, explaining why and how Kramers' theory works from several points of view. Specifically, we consider transitions of a Brownian particle between two potential wells corresponding to the ``reactant'' and the ``product'' of a chemical reaction. A central unifying idea is to divide the equilibrium ensemble of possible states of the system into two sub-ensembles corresponding to the reactant and product states and then to consider fluxes between these sub-ensembles. Importantly, naive separation based on the location measured relative to the barrier top does not result in a mapping that is physically tenable, and instead the past of the trajectory should be considered. Thus constructed reactant and product ensembles provide an internally consistent description of the problem when also viewed from two different perspectives: one based on the definition of the rate as a conditional transition probability per unit time and the other based on the relaxation modes of the time-evolution operator governing the dynamics.

cond-mat.stat-mech↗

arXiv2026

Thermodynamic inference from noisy single-molecule time series

Single-molecule or single-particle tracking measurements inherently yield noisy microscopic trajectories, often significantly constrained by the diffraction limit and by the finite rate at which photons are emitted and counted. Here we study systematically the resulting effects of finite spatial and temporal resolution on one's ability to discern and quantify the arrow of time in microscopic trajectories. Given an experimental time series Y(t) degraded by noise, we consider the problem of estimating the entropy production associated with the corresponding microscopic variable X(t) using two strategies. The first attempts to infer the statistical properties of X(t) from those of Y(t) before estimating the entropy production. The second uses the experimental observable as a proxy for the true microscopic observable, with the entropy production estimator applied directly to Y(t). We prove that both strategies result in lower bounds on the true entropy production. Importantly, noise-degraded observables Y(t) undergo non-Markovian dynamics even when X(t) are Markovian, and non-Markovian entropy production estimators are advantageous. We further note nontrivial interplay between spatial and temporal resolution: in the presence of detection noise, improving the temporal resolution alone may lead to poorer rather than better entropy production estimates.

cond-mat.stat-mech↗

arXiv2026

Energy Barriers for Reversible Chain Scission and Healing under Tension with Displacement Control

Polymer chain scission is a key mechanism for fracture of soft materials. It is well known from single-molecule force spectroscopy experiments that the critical condition for chain scission depends on the loading rate and other environmental effects (e.g., temperature and solvent). Common approaches to describing the kinetics of chain scission often assume force-controlled conditions, that is, when a polymer chain is stretched by a prescribed force. As a result of this assumption, chain scission is irreversible, excluding the possibility of healing. In many soft materials, however, self-healing has been observed after fracture, suggesting possibly reversible chain scission. Here, we show that reversible chain scission is possible under displacement-controlled conditions, that is, when a polymer chain is stretched with a prescribed end-to-end distance. We present a breakable freely-jointed chain model, assuming that a polymer chain breaks when one of its links breaks while the other links remain nearly rigid. At a prescribed end-to-end distance, the free energy of the chain has two local minima and a local maximum (the transition state), giving rise to energy barriers for chain scission and healing. As the prescribed displacement increases, the energy barrier decreases for scission but increases for healing, depending on the chain length (number of links) and the potential energy of the link. With the energy barriers, we adopt a kinetic approach to predict the statistics and kinetics of a single polymer chain under tension, first by integrating the rate equation and then by kinetic Monte Carlo simulations. Notably, the present model predicts rate-dependent chain scission, with a lower bound for the rupture force that could be several orders of magnitude lower than the upper bound (which is close to the theoretical strength of the covalent bonds).

cond-mat.soft↗

arXiv2025

Towards Markov-State Holography

Experiments, in particular on biological systems, typically probe lower-dimensional observables which are projections of high-dimensional dynamics. In order to infer consistent models capturing the relevant dynamics of the system, it is important to detect and account for the memory in the dynamics. We develop a method to infer the presence of hidden states and transition pathways based on observable transition probabilities conditioned on history sequences of visited states for projected (i.e. observed) dynamics of Markov processes. Histograms conditioned on histories reveal information on the transition probabilities of hidden paths locally between any specific pair of observed states. The convergence rate of these histograms towards a stationary distribution provides a local quantification of the duration of memory, which reflects how distinct microscopic paths projecting onto the same observed transition decorrelate in path space. This motivates the notion of "weak Markov order" and provides insight about the hidden topology of microscopic paths in a holography-like fashion. The method can be used to test for the local Markov property of observables. The information extracted is also helpful in inferring relevant hidden transitions which are not captured by a Markov-state model.

cond-mat.stat-mech↗

arXiv2025

What the Boltzmann money game teaches us about statistical mechanics (and maybe economics)

This note explains why a large class of fair, or reversible "money games", i.e., stochastic models of wealth redistribution among agents, lead to steady states described by canonical and microcanonical distributions. The games considered include, for example, ones where more than two agents can be simultaneously involved in money transfers (similarly to many-body collisions in chemical kinetics) and where amounts transferred between agents are random. At the same time, money games that break time reversal symmetry can also lead to the canonical/microcanonical distributions, as illustrated by an explicit example.

physics.chem-ph↗

arXiv2025

Static vs dynamic rough energy landscapes: Where is diffusion faster?

Molecules in dense environments, such as biological cells, are subjected to forces that fluctuate both in time and in space. While spatial fluctuations are captured by Lifson-Jackson-Zwanzig's model of "diffusion in a rough potential", and temporal fluctuations are often viewed as leading to additional friction effects, a unified view where the environment fluctuates both in time and in space is currently lacking. Here we introduce a discrete-state model of a landscape fluctuating both in time and in space. Importantly, the model accounts for the back-reaction of the diffusing particle on the landscape. As a result we find, surprisingly, that many features of the observable dynamics do not depend on the temporal fluctuation timescales and are already captured by the model of diffusion in a rough potential, even though this assumes a static energy landscape.

cond-mat.stat-mech↗

arXiv2025

Hallmarks of Deception in Asset-Exchange Models

We investigate the transient and steady-state dynamics of the Bennati-Dragulescu-Yakovenko money game in the presence of probabilistic cheaters, who can misrepresent their financial status by claiming to have no money. We derive the steady-state wealth distribution per player analytically, and show how the presence of hidden cheaters can be inferred from the relative variance of wealth per player. In scenarios with a finite number of cheaters amidst an infinite pool of honest players, we identify a critical probability of cheating at which the total wealth owned by the cheaters experiences a second-order discontinuity. Below this point, the transition probability to lose money is larger than the probability to gain; conversely, above this point, the direction is reversed. We further establish a threshold cheating probability at which cheaters collectively possess half of the total wealth in the game. Lastly, we provide bounds on the rate at which both cheaters and honest players can gain or lose wealth, contributing to a deeper understanding of deception in asset exchange models.

cond-mat.stat-mech↗

arXiv2024

The significance of fuzzy boundaries of the barrier regions in single-molecule measurements of failed barrier crossing attempts

A recent experimental study reports on measuring the temporal duration and the spatial extent of failed attempts to cross an activation barrier (i.e., "loops") for a folding transition in a single molecule and for a Brownian particle trapped within a bistable potential. Within the model of diffusive dynamics, however, both of these quantities are, on the average, exactly zero because of the recrossings of the barrier region boundary. That is, an observer endowed with infinite spatial and temporal resolution would find that finite loops do not exist (or, more precisely, form a set of measure zero). Here we develop a description of the experiment that takes finite experimental resolution into account and show how the experimental uncertainty of localizing the point, in time and space, where the barrier is crossed leads to observable distributions of loop times and sizes. Although these distributions generally depend on the experimental resolution, this dependence, in certain cases, may amount to a simple resolution-dependent factor and thus the experiments do probe inherent properties of barrier crossing dynamics.

physics.chem-ph↗

arXiv2023

Nonequilibrium statistical mechanics of money/energy exchange models

Many-body dynamical models in which Boltzmann statistics can be derived directly from the underlying dynamical laws without invoking the fundamental postulates of statistical mechanics are scarce. Interestingly, one such model is found in econophysics and in chemistry classrooms: the money game, in which players exchange money randomly in a process that resembles elastic intermolecular collisions in a gas, giving rise to the Boltzmann distribution of money owned by each player. Although this model offers a pedagogical example that demonstrates the origins of Boltzmann statistics, such demonstrations usually rely on computer simulations - a proof of the exponential steady-state distribution in this model has only become available in recent years. Here, we study this random money/energy exchange model, and its extensions, using a simple mean-field-type approach that examines the properties of the one-dimensional random walk performed by one of its participants. We give a simple derivation of the Boltzmann steady-state distribution in this model. Breaking the time-reversal symmetry of the game by modifying its rules results in non-Boltzmann steady-state statistics. In particular, introducing "unfair" exchange rules in which a poorer player is more likely to give money to a richer player than to receive money from that richer player, results in an analytically provable Pareto-type power-law distribution of the money in the limit where the number of players is infinite, with a finite fraction of players in the "ground state" (i.e., with zero money). For a finite number of players, however, the game may give rise to a bimodal distribution of money and to bistable dynamics, in which a participant's wealth jumps between poor and rich states. The latter corresponds to a scenario where the player accumulates nearly all the available money in the game.

cond-mat.stat-mech↗

arXiv2023

Milestoning estimators of dissipation in systems observed at a coarse resolution: When ignorance is truly bliss

Many non-equilibrium, active processes are observed at a coarse-grained level, where different microscopic configurations are projected onto the same observable state. Such "lumped" observables display memory, and in many cases the irreversible character of the underlying microscopic dynamics becomes blurred, e.g., when the projection hides dissipative cycles. As a result, the observations appear less irreversible, and it is very challenging to infer the degree of broken time-reversal symmetry. Here we show, contrary to intuition, that by ignoring parts of the already coarse-grained state space we may -- via a process called milestoning -- improve entropy-production estimates. Milestoning systematically renders observations "closer to underlying microscopic dynamics" and thereby improves thermodynamic inference from lumped data assuming a given range of memory. Moreover, whereas the correct general physical definition of time-reversal in the presence of memory remains unknown, we here show by means of systematic, physically relevant examples that at least for semi-Markov processes of first and second order, waiting-time contributions arising from adopting a naive Markovian definition of time-reversal generally must be discarded.

cond-mat.stat-mech↗

arXiv2019

Transition path dynamics of a nanoparticle in a bistable optical trap

Many processes in chemistry, physics, and biology involve rare events in which the system escapes from a metastable state by surmounting an activation barrier. Examples range from chemical reactions, protein folding, and nucleation events to the catastrophic failure of bridges. A challenge in understanding the underlying mechanisms is that the most interesting information is contained within the rare transition paths, the exceedingly short periods when the barrier is crossed. To establish a model process that enables access to all relevant timescales, although highly disparate, we probe the dynamics of single dielectric particles in a bistable optical trap in solution. Precise localization by high-speed tracking enables us to resolve the transition paths and relate them to the detailed properties of the 3D potential within which the particle diffuses. By varying the barrier height and shape, the experiments provide a stringent benchmark of current theories of transition path dynamics.

physics.chem-ph↗

arXiv2019

Transient probability currents provide upper and lower bounds on non-equilibrium steady-state currents in the Smoluchowski picture

Probability currents are fundamental in characterizing the kinetics of non-equilibrium processes. Notably, the steady-state current $J_{ss}$ for a source-sink system can provide the exact mean-first-passage time (MFPT) for the transition from source to sink. Because transient non-equilibrium behavior is quantified in some modern path sampling approaches, such as the "weighted ensemble" strategy, there is strong motivation to determine bounds on $J_{ss}$ -- and hence on the MFPT -- as the system evolves in time. Here we show that $J_{ss}$ is bounded from above and below by the maximum and minimum, respectively, of the current as a function of the spatial coordinate at any time $t$ for one-dimensional systems undergoing over-damped Langevin (i.e., Smoluchowski) dynamics and for higher-dimensional Smoluchowski systems satisfying certain assumptions when projected onto a single dimension. These bounds become tighter with time, making them of potential practical utility in a scheme for estimating $J_{ss}$ and the long-timescale kinetics of complex systems. Conceptually, the bounds result from the fact that extrema of the transient currents relax toward the steady-state current.

cond-mat.stat-mech↗

arXiv2009

Influence of Local and Residual Structures on the Scaling Behavior and Dimensions of Unfolded Proteins

Although recent spectroscopic studies of chemically denatured proteins hint at significant nonrandom residual structure, the results of extensive small angle X-ray scattering studies suggest random coil behavior, calling for a coherent understanding of these seemingly contradicting observations. Here, we report the results of a Monte Carlo study of the effects of two types of local structures, a helix and Polyproline II (PPII) helix, on the dimensions of random coil polyalanine chains viewed as a model of highly denatured proteins. With an alpha helix content of 20%, corresponding to the Ramachandran probability of being in the helical basin, experimentally observed radii of gyration are recovered. Experimental radii are similarly recovered at an a helix content of 87%, providing an explanation for the previously puzzling experimental finding that the dimensions of the highly helical methanol-induced unfolded state are experimentally indistinguishable from those of the helix-poor urea-unfolded state. In contrast, the radius of gyration increases monotonically with increasing PPII content, and is always more expanded than the dimensions observed experimentally. These results suggest that PPII is unlikely the sole, dominant preferred conformation for unfolded proteins.

physics.bio-ph↗

arXiv2006

Untying molecular friction knots

Motivated by recent advances in single molecule manipulation techniques that enabled several groups to tie knots in individual polymer strands and to monitor their dynamics, we have used computer simulations to study "friction knots" joining a pair of polymer strands. The key property of a friction knot splicing two ropes is that it becomes jammed when the ropes are pulled apart. In contrast, molecular friction knots eventually become undone by thermal motion. We show that depending on the knot type and on the polymer structure, a friction knot between polymer strands can be strong (the time t the knot stays tied increases with the force F applied to separate the strands) or weak (t decreases with increasing F). We further present a simple model explaining these behaviors.

physics.bio-ph↗

arXiv1997

Van der Waals Energies in Density Functional Theory

In principle, density functional theory yields the correct ground-state densities and energies of electronic systems under the action of a static external potential. However, traditional approximations fail to include Van der Waals energies between separated systems. This paper proposes a practical procedure for remedying this difficulty. Our method allows seamless calculations between small and large inter-system distances. The asymptotic H-He and He--He interactions are calculated as a first illustration, with very accurate results.

cond-mat↗