Ontology of temperature in nonequilibrium systems

The laws of thermodynamics provide a clear concept of the temperature for an equilibrium system in the continuum limit. Meanwhile, the equipartition theorem allows one to make a connection between the ensemble average of the kinetic energy and the uniform temperature. When a system or its environment is far from equilibrium, however, such an association does not necessarily apply. In small systems, the regression hypothesis may not even apply. Herein, it is shown that in small nonequilibrium systems, the regression hypothesis still holds, though with a generalized definition of the temperature. The latter must now be defined for each such manifestation.     

The protein folding transition state: insights from kinetics and thermodynamics

We perform extensive lattice Monte Carlo simulations of protein folding to construct and compare the equilibrium and the kinetic transition state ensembles of a model protein that folds to the native state with two-state kinetics. The kinetic definition of the transition state is based on the folding probability analysis method, and therefore on the selection of conformations with 0.4相似文献   

Thermodynamic derivations of conditions for chemical equilibrium and of Onsager reciprocal relations for chemical reactors

For an isolated chemical reactor, we derive the conditions for chemical equilibrium in terms of either energy, volume, and amounts of constituents or temperature, pressure, and composition, with special emphasis on what is meant by temperature and chemical potentials as the system proceeds through nonequilibrium states towards stable chemical equilibrium. For nonequilibrium states, we give both analytical expressions and pictorial representations of the assumptions and implications underlying chemical dynamics models. In the vicinity of the chemical equilibrium state, we express the affinities of the chemical reactions, the reaction rates, and the rate of entropy generation as functions of the reaction coordinates and derive Onsager reciprocal relations without recourse to statistical fluctuations, time reversal, and the principle of microscopic reversibility.     

Statistical mechanical theory for steady state systems. V. Nonequilibrium probability density

The phase space probability density for steady heat flow is given. This generalizes the Boltzmann distribution to a nonequilibrium system. The expression includes the nonequilibrium partition function, which is a generating function for statistical averages and which can be related to a nonequilibrium free energy. The probability density is shown to give the Green-Kubo formula in the linear regime. A Monte Carlo algorithm is developed based upon a Metropolis sampling of the probability distribution using an umbrella weight. The nonequilibrium simulation scheme is shown to be much more efficient for the thermal conductivity of a Lennard-Jones fluid than the Green-Kubo equilibrium fluctuation method. The theory for heat flow is generalized to give the generic nonequilibrium probability densities for hydrodynamic transport, for time-dependent mechanical work, and for nonequilibrium quantum statistical mechanics.     

An Energy Interconversion Principle Applied in Reaction dynamics for the determination of equilibrium standard states

Chemical and other reaction theories involving thermodynamical equilibrium states utilize statistical mechanical equilibrium density distributions. Here, a definition of heat-work transformation termed thermo-mechanical coherence is first made, and it is conjectured that most molecular bonds have the above heat-work transformation property, which models a chemical bond as a “centrifugal heat engine”, where the internal energy state need not correspond to any of the standard equilibrium densities. Expressions are derived for the standard Gibbs free energy, enthalpy, and entropy where the bond coordinates need not conform to a non-degenerate Boltzmann state, since bond breakdown and formation are processes that have direction, whereas equilibrium distributions are derived when the Hamiltonian is of fixed form, which is not the case for chemical reactions using localized Hamiltonians. The empirically determined Gibbs free energy from a known molecular dynamics simulation of a dimer reaction , accords rather well with the theoretical estimate. A relation connecting the rate of reaction with the equilibrium constant and other kinetic parameters is derived and could place the commonly observed linear relationship between the logarithms of the rate constant and equilibrium constant on a firmer theoretical footing. These relationships could include analogues of the Hammett correlations used extensively in physical organic chemistry, as well as others which are temperature dependent. One prediction of the principles developed here is that the equilibrium standard reaction free energy is more dependent on the height of the intermolecular potential than its depth, so that the sign of the ΔG ^θ can change for varying barrier height with fixed well depth, which may appear counter-intuitive. All the above developments can be tested directly in simulations and therefore provides a fertile ground for further research with significant implications on how standard states are determined in relation to the direction of chemical reaction.This work treats the molecular bond using standard thermodynamics as if it were a system, and it is anticipated that with the advent of single-molecule science and experiment, that might be one direction in which molecular statistical thermodynamics would develop.     

Asymptotic separability of three-body continuum wave functions for Coulomb systems

We consider a general three-body Coulomb system above the threshold for total break-up. For large particle separations the Schrödinger equation for this system is shown to be separable in terms of new suitably defined 6-dimensional parabolic coordinates. Although these coordinates are not orthogonal, mixed second derivative terms in the expression for the kinetic energy do not contribute at large particle separations to the Coulomb modification of free particle states. Rejection of mixed second derivatives at all particle configurations yields a three-body continuum wave function that satisfies exact asymptotic boundary conditions for Coulomb systems and treats all two-body interactions fully symmetric. This analysis splits the wave equation into an ‘unperturbed’ part plus a perturbation where the unperturbed part takes into account all long-range correlations.     

Nonequilibrium potential function of chemically driven single macromolecules via Jarzynski-type Log-Mean-Exponential Heat

Applying the method from recently developed fluctuation theorems to the stochastic dynamics of single macromolecules in ambient fluid at constant temperature, we establish two Jarzynski-type equalities: (1) between the log-mean-exponential (LME) of the irreversible heat dissiption of a driven molecule in nonequilibrium steady-state (NESS) and ln P(ness)(x) and (2) between the LME of the work done by the internal force of the molecule and nonequilibrium chemical potential function mu(ness)(x) identical with U(x) + k(B)T ln P(ness)(x), where P(ness)(x) is the NESS probability density in the phase space of the macromolecule and U(x) is its internal potential function. Psi = integral mu(ness)(x) P(ness)(x) dx is shown to be a nonequilibrium generalization of the Helmholtz free energy and DeltaPsi = DeltaU - TDeltaS for nonequilibrium processes, where S = - kB integralP(x) ln P(x) dx is the Gibbs entropy associated with P(x). LME of heat dissipation generalizes the concept of entropy, and the equalities define thermodynamic potential functions for open systems far from equilibrium.     

Using non-Gaussian density functional fits to improve relative free energy calculations

The accurate and reliable computation of relative free energy differences remains an important long-term goal. Major stumbling blocks for achieving this goal reflect the difficulty of sampling in a known fashion along the reaction coordinate and of maximally combining information that has been collected from the simulation along the reaction coordinate. In this paper we examine the utility of a probability density functional type fit to the distribution of work events collected during a nonequilibrium sample along the reaction coordinate. This approach can readily be generalized to equilibrium sampling and has the potential to estimate the quality of a relative free energy estimate as data are being collected. The method may have the greatest utility for nonequilibrium sampling where non-Gaussian work distributions are generally present that are strongly dominated by rare event sampling in the tail region. We believe that the approach can be used to augment the design and the error analysis of relative free energy computations thus improving the ability to reliably and with known accuracy compute a relative free energy.     

End-evaporation dynamics revisited

We present analytical results on the so-called end-evaporation kinetics in equilibrium polymeric systems following a temperature jump (T jump). A T jump prepares the system with a nonequilibrium length distribution, after which it relaxes back to its equilibrium state. Starting from a master equation, we develop a mean-field analytical theory based on a generating function approach, which allows explicit approximate expressions for the monomer and dimer concentrations to be derived in a discrete setting; the concentrations of the other chains as well as the average chain length were shown to be entirely expressible in terms of the monomer and dimer concentrations. We find that the calculated monomer and dimer concentrations as well as the average chain length are in good agreement with numerical simulation results and do not suffer from some of the defects of earlier continuum theories. Furthermore, the relaxation was shown to take place in three different stages. The first stage comprises the very fast relaxation of the monomers to almost their equilibrium concentration; the other polymer chains have hardly relaxed. During the second stage, which is highly nonlinear, a redistribution of material at practically constant monomer density takes place. Only in the final stage of the relaxation process the chain concentrations approach their true equilibrium values. In this stage there are only very small shifts in the concentrations of chains, which are governed by extremely slow "indirect" monomer-mediated processes.     

Statistical mechanical theory for the structure of steady state systems: application to a Lennard-Jones fluid with applied temperature gradient

The constrained entropy and probability distribution are given for the structure that develops in response to an applied thermodynamic gradient, as occurs in driven steady state systems. The theory is linear but is applicable to gradients with arbitrary spatial variation. The phase space probability distribution is also given, and it is surprisingly simple with a straightforward physical interpretation. With it, all of the known methods of equilibrium statistical mechanics for inhomogeneous systems may now be applied to determining the structure of nonequilibrium steady state systems. The theory is illustrated by performing Monte Carlo simulations on a Lennard-Jones fluid with externally imposed temperature and chemical potential gradients. The induced energy and density moments are obtained, as well as the moment susceptibilities that give the rate of change of these with imposed gradient and which also give the fluctuations in the moments. It is shown that these moment susceptibilities can be written in terms of bulk susceptibilities and also that the Soret coefficient can be expressed in terms of them.     

Configurational temperature control for atomic and molecular systems

A new configurational temperature thermostat suitable for molecules with holonomic constraints is derived. This thermostat has a simple set of motion equations, can generate the canonical ensemble in both position and momentum space, acts homogeneously through the spatial coordinates, and does not intrinsically violate the constraints. Our new configurational thermostat is closely related to the kinetic temperature Nosé-Hoover thermostat with feedback coupled to the position variables via a term proportional to the net molecular force. We validate the thermostat by comparing equilibrium static and dynamic quantities for a fluid of n-decane molecules under configurational and kinetic temperature control. Practical aspects concerning the implementation of the new thermostat in a MOLECULAR DYNAMICS code and the potential applications are discussed.     

Nonequilibrium effects in thermal plasma chemistry

Numerical calculations have been performed to assess the potential significance of nonequilibrium effects on chemical reactivity in thermal plasmas The calculations consider situations in which the electron temperature and/or the electron density are elevated above their equilibrium values corresponding to the local gas temperature. Such nonequilibrium may occur in the plasma torch itself or could be purposefully imposed by a controlled hybrid discharge in a downstream reactor region so as to augment reactivity over a longer residence time. The calculations account for finite ionization/recombination rates of atomic and molecular species, electron-impact dissociation, dissociative recombination, dissociative attachment, and predissociation effects, as well as thermal reactions between neutral chemical species. As an example of the possible nonequilibrium enhancement of molecular decomposition, initial consideration has focused on the dissociation rates of diatomic species where heavy particle reaction rates and cross sections can be reasonably estimated. The results show that for O₂ or H₂ in argon at moderate temperatures, electron-temperature elevation can give rise to a notable enhancement of the dissociation rate, in comparison with the equilibrium case. Depending on the situation, it is found that either relatively energetic electron-impact dissociation or dissociative attachment (for O₂) can dominate the enhanced dissociation rate—which can be more than a factor of 2 greater than in the absence of a discharge. Similar effects would be expected for the decomposition of more complicated molecules.     

Essential energy space random walks to accelerate molecular dynamics simulations: convergence improvements via an adaptive-length self-healing strategy

Recently, accelerated molecular dynamics (AMD) technique was generalized to realize essential energy space random walks so that further sampling enhancement and effective localized enhanced sampling could be achieved. This method is especially meaningful when essential coordinates of the target events are not priori known; moreover, the energy space metadynamics method was also introduced so that biasing free energy functions can be robustly generated. Despite the promising features of this method, due to the nonequilibrium nature of the metadynamics recursion, it is challenging to rigorously use the data obtained at the recursion stage to perform equilibrium analysis, such as free energy surface mapping; therefore, a large amount of data ought to be wasted. To resolve such problem so as to further improve simulation convergence, as promised in our original paper, we are reporting an alternate approach: the adaptive-length self-healing (ALSH) strategy for AMD simulations; this development is based on a recent self-healing umbrella sampling method. Here, the unit simulation length for each self-healing recursion is increasingly updated based on the Wang-Landau flattening judgment. When the unit simulation length for each update is long enough, all the following unit simulations naturally run into the equilibrium regime. Thereafter, these unit simulations can serve for the dual purposes of recursion and equilibrium analysis. As demonstrated in our model studies, by applying ALSH, both fast recursion and short nonequilibrium data waste can be compromised. As a result, combining all the data obtained from all the unit simulations that are in the equilibrium regime via the weighted histogram analysis method, efficient convergence can be robustly ensured, especially for the purpose of free energy surface mapping.     

A discussion on an apparent MO theory paradox

A discussion on an apparent MO theory paradox, concerning the probability of positioning a particle within a nodal plane, is carried out in terms of particle confinement probability within finite thickness slabs encompassing the plane in question. It is also discussed how using extended wave functions, the joint position plus kinetic resultant probability distribution, just fulfilling the uncertainty principle, produces a compensating effect on the particle probability of sharing position or momentum within the two half‐spaces delimited by the considered nodal plane. This revised version was published online in July 2006 with corrections to the Cover Date.     

Simulating the relaxation dynamics of microwave-driven zeolites

We have performed equilibrium and nonequilibrium molecular dynamics simulations to study how microwave (MW)-heated zeolite systems relax to thermal equilibrium. We have simulated the relaxation of both ionic and dipolar phases in FAU-type zeolites, finding biexponential relaxation in all cases studied. Fast-decay times were uniformly below 1 ps, while slow-decay times were found to be as long as 14 ps. Fast-decay times increase with an increase in the initial temperature difference between MW-heated ions/dipoles and the equilibrium system. Slow-decay times were found to be relatively insensitive to the details of the MW-heated nonequilibrium state. Velocity, force, and orientational correlation functions, calculated at equilibrium to explore the natural dynamics of energy transfer, decay well before 1 ps and show little evidence of biexponential decay. In contrast, kinetic energy correlation functions show strong biexponential behavior with slow-decay times as long as 14 ps. We suggest a two-step mechanism involving initial, efficient energy transfer mediated by strongly anharmonic zeolite-guest forces, followed by a slower process mediated by weakly anharmonic couplings among normal modes of the zeolite framework. In addition to elucidating relaxation from MW-heated states, we expect that these studies will shed light on energy transfer in other contexts, such as adsorption and reaction in zeolites, which often involve significant heat release.