Violation Of Detailed Balance Research Articles

A Monte Carlo Simulation Scheme for Nonideal Dendrimers Satisfying Detailed Balance

We present a configurational-biased lattice Monte Carlo scheme for simulating nonideal dendrimers that satisfies detailed balance. This corrects an important shortcoming in a previous lattice Monte Carlo scheme by Mansfield and Klushin: in a previous publication, we showed that the Mansfield and Klushin scheme did not obey detailed balance, and that this led to surprisingly large errors in the radius of gyration Rg and scattering form factor P(q) for ideal dendrimers. In this paper, we have calculated the radius of gyration, the form factor, and the intramolecular density profile for g = 1−8 self-avoiding dendrimers and find that our results are qualitatively the same as previous results obtained by Mansfield and Klushin (g is the generation number). This indicates that the error in the Mansfield and Klushin scheme due to detailed balance violation is much smaller for self-avoiding dendrimers. Our other key conclusions concerning the equilibrium properties of self-avoiding dendrimers are the following: ...

Non-equilibrium stationary state of a two-temperature spin chain

A kinetic one-dimensional Ising model is coupled to two heat baths, such that spins at even (odd) lattice sites experience a temperature Te (To). Spin-flips occur with Glauber-type rates generalized to the case of two temperatures. Driven by the temperature differential, the spin chain settles into a non-equilibrium steady state which corresponds to the stationary solution of a master equation. We construct a perturbation expansion of this master equation in terms of the temperature difference and compute explicitly the first two corrections to the equilibrium Boltzmann distribution. The key result is the emergence of additional spin operators in the steady state, increasing in spatial range and order of spin products. We comment on the violation of detailed balance and entropy production in the steady state.

N 2 dissociative adsorption on Ru(0001): The role of energy loss

New molecular beam experiments on the dissociation probability S0 for N2 on Ru(0001) are presented. These are in general agreement with prior measurements and exhibit very unusual behavior; a very slow increase of S0 with incident kinetic energy E and the fact that S0 is still only ∼10−3 at incident energies considerably above the barrier. A simple dynamical model is developed to describe this unusual sticking behavior. The key aspect is that there is considerable energy loss Δ from E upon initial impact with the surface (principally to the lattice) and only E−Δ is then available to surmount the activation barrier in the exit channel. Using experimentally measured values of Δ from scattering experiments gives good qualitative agreement of this model with the measured S0. One implication of the strong energy loss is that there is an apparent violation of detailed balance when comparing only the reactive fluxes of activated adsorption and associative desorption.

The Effects of Non-Identifiability on Testing for Detailed Balance in Aggregated Markov Models for Ion-Channel Gating

Aggregated Markov models are a widely used tool to model patch clamp data measured from single ion channels. These channels must obey the principle of detailed balance in thermodynamic equilibrium; otherwise, the channel is driven by an external source of energy. We investigate the power of a likelihood ratio test for detailed balance for a number of data points which is in the order of magnitude of patch clamp experiments. We show that for certain models with nearly equal dwell times, a test for detailed balance suffers from a loss of power to detect violations of detailed balance which is due to the non-identifiability of the transition rates for models with equal dwell times.

Phase diagram and storage capacity of sequence processing neural networks

We solve the dynamics of Hopfield-type neural networks which store sequences of patterns, close to saturation. The asymmetry of the interaction matrix in such models leads to violation of detailed balance, ruling out an equilibrium statistical mechanical analysis. Using generating functional methods we derive exact closed equations for dynamical order parameters, viz. the sequence overlap and correlation- and response functions, in the thermodynamic limit. We calculate the time translation invariant solutions of these equations, describing stationary limit-cycles, which leads to a phase diagram. The effective retarded self-interaction usually appearing in symmetric models is here found to vanish, which causes a significantly enlarged storage capacity of $\alpha_c\sim 0.269$, compared to $\alpha_\c\sim 0.139$ for Hopfield networks storing static patterns. Our results are tested against extensive computer simulations and excellent agreement is found.

Critical behavior of O(n)-symmetric systems with reversible mode-coupling terms: Stability against detailed-balance violation

We investigate nonequilibrium critical properties of O(n)-symmetric models with reversible mode-coupling terms. Specifically, a variant of the model of Sasv\'ari, Schwabl, and Sz\'epfalusy (SSS) is studied, where violation of detailed balance is incorporated by allowing the order parameter and the dynamically coupled conserved quantities to be governed by heat baths of different temperatures ${\mathrm{T}}_{\mathrm{S}}$ and ${\mathrm{T}}_{\mathrm{M}}$, respectively. Dynamic perturbation theory and the field-theoretic renormalization group are applied to one-loop order, and yield two new fixed points in addition to the equilibrium ones. The first fixed point corresponds to \ensuremath{\Theta}=${\mathrm{T}}_{\mathrm{S}}$/${\mathrm{T}}_{\mathrm{M}}$=\ensuremath{\infty} and leads to model A critical behavior for the order parameter and to anomalous noise correlations for the generalized angular momenta; the second one is at \ensuremath{\Theta}=0 and is characterized by mean-field behavior of the conserved quantities, by a dynamic exponent z=d/2 equal to that of the equilibrium SSS model, and by modified static critical exponents. However, both these new fixed points are unstable, and upon approaching the critical point detailed balance is restored, and the equilibrium static and dynamic critical properties are recovered.

A dynamically and kinetically consistent mechanism for H2 adsorption/desorption from Si(100)-2 x 1.

Curiously, ${\mathrm{H}}_{2}$ desorption from Si(100)-2\ifmmode\times\else\texttimes\fi{}1 follows approximately first-order kinetics rather than the expected second-order kinetics, arousing interest about the mechanism involved in the desorption process. We investigate the energetics and rate constants of three proposed mechanisms for ${\mathrm{H}}_{2}$ desorption from Si(100)-2\ifmmode\times\else\texttimes\fi{}1, namely, the prepairing mechanism, the isomerization mechanism, and the isolated dihydride mechanism, using complete active space self-consistent-field and multireference single- and double-excitation configuration-interaction calculations. We find the desorption barrier for the isolated dihydride mechanism to be 2.49 eV, the only barrier in excellent agreement with the experimentally determined barrier (\ensuremath{\sim}2.5 eV). The isolated dihydride mechanism also provides the only calculated desorption rate constant close to experimental values. Finally, we show that this mechanism is able to explain the experimentally observed apparent violation of detailed balance of ${\mathrm{H}}_{2}$ adsorption/desorption on Si(100), as well as other experimentally observed dynamics. \textcopyright{} 1996 The American Physical Society.

TIME-REVERSAL DUALITY AND PLANAR LATTICE DUALITY IN NON-EQUILIBRIUM LATTICE MODELS

The contact process (CP) is a simple mathematical model for the spread of infection of a contagious disease. Though it has only nearest-neighbor interactions, phase transitions occur even in the one-dimensional system and non-equilibrium stationary states appear in supercritical phase. This implies violation of detailed balance. The appearance of such non-equilibrium states is related to directed percolation problems on the spatiotemporal plane. In the present paper, we study discretetime versions of the CP, the two-neighbor stochastic cellular automata (SCA), and clarify this viewpoint. We use two kinds of duality relations, the time-reversal duality and the planar lattice duality on the spatio-temporal plane, and give a good lower bound for the critical line of non-equilibrium phase transitions in the two-neighbor SCA.

Ab initio explanation of the apparent violation of detailed balance for H2 adsorption/desorption from Si(100)

Abstract The experimentally observed apparent violation of detailed balance in the adsorption and desorption of H2 on Si(100)-2 × 1 is explained via a dihydride intermediate that can be accessed via two different transition states, as found by complete active space self-consistent field/multireference single and double excitation configuration interaction (CASSCF/MRSDCI) calculations. Our calculations explain the low sticking probability by predicting an early symmetric transition state to adsorption with a high barrier. We predict that desorption, on the other hand, occurs through an asymmetric transition state and find excellent agreement between our calculated barrier to desorption and experimental values. For the asymmetric transition state we calculate a small barrier to adsorption, however, we suggest that impinging H2 seldom sees this orientationally constrained late transition state to adsorption, explaining the apparent violation of detailed balance.

D2 dissociative adsorption on and associative desorption from Si(100): Dynamic consequences of an ab initio potential energy surface

Dynamical calculations are reported for D2 dissociative chemisorption on and associative desorption from a Si(100) surface. These calculations use the dynamically relevant effective potential which is based on an ab initio potential energy surface for the ‘‘pre-paired’’ species. Three coordinates are included dynamically; the distance to the surface, the D–D bond length and a Si phonon coordinate. Other coordinates (multidimensionality) have been included via a static approximation. Both an asymmetric and symmetric reaction paths are considered. While energetics favors the asymmetric path, phase space favors the symmetric one. Under the conditions of many experiments, either could dominate. The calculations show quite weak dynamic coupling to the Si lattice for both paths, i.e., weak surface temperature dependences to dissociation and small energy loss to the lattice upon desorption. These calculations do not support previous suggestions that either a strong coupling to the lattice or ‘‘entropic’’ effects can reconcile the apparent violation of detailed balance obtained by comparing experimental dissociation to desorption barriers. In fact, the results reported here do not agree with several experimental findings. We discuss several possibilities for this disagreement, including experimental artifact, limitations in the dynamical model and even the possibility that electronically adiabatic dynamics involving the ‘‘pre-paired’’ species is not relevant to experiments on real systems.

Long-time tails in lattice gases violating detailed balance.

Using analytic and simulation techniques, we study the long- and intermediate-time behavior of the velocity autocorrelation function in two-dimensional lattice gas automata with stationary states that violate detailed balance. Such models are prototypes of dissipative systems, have stationary states that are very different from Gibbs states, and exhibit long range spatial correlations. Such static correlations are absent in models with detailed balance symmetry. In some lattice gases with strong violation of detailed balance, the simulations show negative velocity correlations at intermediate times (cage effect), which, to our knowledge, has never been observed in lattice gases before. A mode coupling calculation is used to analyze the long-time tail, whose amplitude is very different from the mean field prediction. When the above static correlations are taken into account, our theoretical predictions agree very well with the results of computer simulations.

Discrete fluctuators and broadband noise in the charge-density wave in NbSe3.

In small samples of ${\mathrm{NbSe}}_{3}$ the broadband noise of the sliding charge-density wave (CDW) can be partially resolved into two-state and multistate fluctuators, which show strong sensitivity to the bias current and temperature. Explicit violations of detailed balance appear. Near the threshold bias for sliding, intermittent periods of noise occur, indicating that some or all of the sample fluctuates between the pinned and sliding states. The behavior of the discrete fluctuators under a variety of time-dependent bias conditions indicates that some particular configurations are available for the CDW in both sliding and pinned states, but with slower dynamics in the pinned state. The results are consistent with a model in which the noise comes from collective rearrangements of defects in the CDW.

Oscillations, Stability, and Equilibrium in Magnetic Exchange Networks

Abstract The generalized N-site magnetic exchange network is described by coupled Bloch equations whose solution is in general stable and characterized by eigenvalues with negative real parts. The analysis of this system is greatly simplified when detailed balance is satisfied, being described by an exchange matrix with eigenvalues that are negative and purely real. Consequently, the multiple-site system in detailed balance approaches its equilibrium condition by purely exponential relaxation. In addition, satisfaction of detailed balance requires that the stationary solution of the Bloch equations describing the longitudinal magnetization of a spin be the equilibrium magnetization of that spin. Violation of detailed balance with cyclic exchange results in the relaxation of the system taking the form of a damped oscillatory function, with the amount of damping generally decreasing as the number of sites increases.

Phillips and Chrzan reply.

The authors argue that the non-KPZ (Kardar-Parisi-Zhang) phase in thei model arises not from the violation of detailed balance, but from the absence of desorption at low temperatures. (AIP)Received 10 February 1992DOI:https://doi.org/10.1103/PhysRevLett.68.2855©1992 American Physical Society

Possible forms for dwell-time histograms from single-channel current records

Certain macromolecules embedded in the cell membranes of a variety of cells behave as gated ion-selective pores or channels. The length of time that a channel remains open or closed is not deterministic in nature and must be described in terms of relative probabilities. If channels act independently of each other and appropriate experimental conditions can be maintained, the behavior of a channel can be described by a homogeneous Markov process. Using this representation, the relative probability of observing openings (or closings) of various durations can be described by a sum of discrete components which are related to the underlying model of the kinetic behavior of the channel. Generally, these discrete components are taken to be simple decaying exponentials; however, exponentially decaying oscillatory components (as well as certain others which are discussed) are consistent with the Markov process representation. The presence of components other than simple decaying exponentials is shown to imply the violation of detailed balance in the steady-state (which requires energy), and thus, the presence of cyclic pathways in models which accurately represent the kinetic behavior of the channel. Oscillatory components, if present, will in general decay at a faster rate than the slowest decaying component, which, except under a very restricted set of conditions, will be a simple exponential.

On Violation of Detailed Balance of Fluctuation in an Oscillatory System

Stochastic behavior of a nonlinear oscillatory system is studied in a coordinate frame rotating with a fundamental frequency. It is shown that reactive property of nonlinearity of an oscillatory system is a cause of a violation of detailed balance of the fluctuation arround the steady state far from equilibrium. Whereas, even in the steady state far from equilibrium, the detailed balance of the fluctuation arround a circular secular motion can be established, if a phase of self-sustained oscillation is locked by the external force having particular strength.

Effect of VV Transfer on the Rate of Diatomic Dissociation

The effect of VV transfer processes on the rate of thermal dissociation of diatomic molecules is considered within the steady-state approximation for a single-quantum step master equation. An accurate rate law is obtained for the truncated harmonic oscillator through replacement of the agents for VV transfer by the vibrational energy. Approximate numerical solutions for a Morse oscillator model of the representative species O2, H2, and HCl are in quite satisfactory agreement with the measured rates and provide at least qualitative explanations for nearly all the unusual features of the measurements. The rate enhancement effect of VV transfer is found to be slight; the primary, and quite general consequence of VV transfer is rather a depression of the rate, especially at high temperatures, which then appears as a considerable reduction in activation energy. This effect is shown to arise from a violation of detailed balance for the VV processes whenever the vibrational energy is depleted by rapid dissociation.

T-violation and detailed balance in direct reactions

The relationship between detailed balance violation in direct reactions and the matrix elements of the T-odd part of H between different target or residual states is calculated. Presently available experiments put a limiting value of 25 keV on the magnitudes of these matrix elements.