Configurational Temperature, Verification of Monte Carlo Simulations

[Unable to convert symbols, please look at PDF version for symbols] A new diagnostic that is useful for checking the algorithmic correctness of Monte Carlo computer programs is presented. The check is made by comparing the Boltzmann temperature, which is input to the program and used to accept or reject moves, with a configurational temperature k T B config [unable to convert symbol, please see PDF]. Here, F is the potential energy of the system and [symbal]represents the dimensionless gradient operator with respect to the particle positions [symbol]. We show, using a simulation of Lennard-Jones particles, that the configurational temperature rapidly and accurately tracks changes made to the input temperature even when the system is not in global thermodynamic equilibrium. Coding and/or algorithmic errors can be detected by checking that the input temperature and Tconfig agree. The effects of system size and continuity of F and its first derivative on Tconfig are also discussed

Tractable molecular theory of transport of Lennard-Jones fluids in nanopores

We present here a tractable theory of transport of simple fluids in cylindrical nanopores, which is applicable over a wide range of densities and pore sizes. In the Henry law low-density region the theory considers the trajectories of molecules oscillating between diffuse wall collisions, while at higher densities beyond this region the contribution from viscous flow becomes significant and is included through our recent approach utilizing a local average density model. The model is validated by means of equilibrium as well nonequilibrium molecular dynamics simulations of supercritical methane transport in cylindrical silica pores over a wide range of temperature, density, and pore size. The model for the Henry law region is exact and found to yield an excellent match with simulations at all conditions, including the single-file region of very small pore size where it is shown to provide the density-independent collective transport coefficient. It is also shown that in the absence of dispersive interactions the model reduces to the classical Knudsen result, but in the presence of such interactions the latter model drastically overpredicts the transport coefficient. For larger micropores beyond the single-file region the transport coefficient is reduced at high density because of intermolecular interactions and hindrance to particle crossings leading to a large decrease in surface slip that is not well represented by the model. However, for mesopores the transport coefficient increases monotonically with density, over the range studied, and is very well predicted by the theory, though at very high density the contribution from surface slip is slightly overpredicted. It is also seen that the concept of activated diffusion, commonly associated with diffusion in small pores, is fundamentally invalid for smooth pores, and the apparent activation energy is not simply related to the minimum pore potential or the adsorption energy as generally assumed. (C) 2004 American Institute of Physics

The fluctuation theorem and Lyapunov weights

The Fluctuation Theorem (FT) is a generalisation of the Second Law of Thermodynamics that applies to small systems observed for short times. For thermostatted systems it gives the probability ratio that entropy will be consumed rather than produced. In this paper we derive the Transient and Steady State Fluctuation Theorems using Lyapunov weights rather than the usual Gibbs weights. At long times the Fluctuation Theorems so derived are identical to those derived using the more standard Gibbs weights.Comment: 26 pages; to appear in Physica

Homogeneous shear flow of a hard-sphere fluid: Analytic solutions

Recently, a solution for collision-free trajectories in an N particle thermostatted hard-sphere system undergoing homogeneous shear (the so-called "Sllod" equations of motion) led to a kinetic theory of dilute hard-sphere gases under shear. However, a solution for collisions, necessary for a complete theory at higher densities, has been missing. We present an analytic solution to this problem, which provides surprising insights into the mechanical aspects of thermostatting a system in an external field. The equivalence of constant temperature and constant energy ensembles in the thermodynamic limit in equilibrium, the conditions for the nature of heat exchange with the environment (entropy creation and reduction) in the system, and the condition for appearance of the artificial string phase follow from our solution

On the validity of Fouriers law in systems with spatially varying strain rates

Non-equilibrium molecular dynamics (NEMD) simulations are used to study the generation of heat fluxes in systems with spatially varying shear rates. We show that the kinetic temperature, when used in Fourier's law of heat conduction, does not correctly account for the heat flux, and that the normal temperature as described by Rugh (1997, Phys. Rev. Lett., 78, 772), should be used. Only in the absence of normal temperature gradients can heat fluxes due to strain rate coupling be correctly calculated

Homogeneous shear flow of a hard-sphere fluid: Analytic solutions

The analytical solutions for collision free trajectories in an N particle thermostatted hard-sphere system undergoing homogeneous shear were discussed. The solutions led to the equivalence of constant temperature and constant energy ensembles in the thermodynamic limit in equilibrium and the conditions for the nature of heat exchange with the environment in the system. The condition for appearance of the artificial string phase also followed from the solutions

A dynamical-systems interpretation of the dissipation function, T-mixing and their relation to thermodynamic relaxation

We review the notions of the dissipation function and T-mixing for noninvariant measures, recently introduced for nonequilibrium molecular dynamics models. We provide a dynamical-systems interpretation for the dissipation function and related results, providing new perspectives into results such as the second-law inequality. We then consider the problem of relaxation within this framework—the convergence of time averages along single phase– space trajectories, as opposed to the convergence of ensemble averages. As a first step in this direction, we observe that T-mixing implies convergence to a unique asymptotic ensemble, independent on the initial ensemble. In particular, the initial ensemble can be concentrated arbitrarily closely to any point in phase–space

Method for determining the shear stress in cylindrical systems

We develop a method for determining the elements of the pressure tensor at a radius r in a cylindrically symmetric system, analogous to the so-called “method of planes” used in planar systems [B. D. Todd, Denis J. Evans, and Peter J. Daivis, Phys. Rev. E 52, 1627 (1995)]. We demonstrate its application in determining the radial shear stress dependence during molecular dynamics simulations of the forced flow of methane in cylindrical silica mesopores. Such expressions are useful for the examination of constitutive relations in the context of transport in confined systems

Microscopic expressions for the thermodynamic temperature

We show that arbitrary phase space vector fields can be used to generate phase functions whose ensemble averages give the thermodynamic temperature. We describe conditions for the validity of these functions in periodic boundary systems and the molecula