A 'non-classical' information theory of spectral line shape

“…11 are consistent with the higher moments being larger than those of a gaussian. [60][61][62][63][64] The effect of shear is also to skew the PDF to the right. The figure also shows that the data for sphere and cubes fall on the same lines, so the magnitude of the subvolume, Ω, rather than its shape (within reasonable limits) is the key governing factor for this local stress model.…”

Section: A Nemd Results and The Fluctuation Theoremmentioning

confidence: 99%

Incremental viscosity by non-equilibrium molecular dynamics and the Eyring model

Heyes

Dini

Smith

2018

The Journal of Chemical Physics

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The viscoelastic behavior of sheared fluids is calculated by Non-Equilibrium Molecular Dynamics (NEMD) simulation, and complementary analytic solutions of a time-dependent extension of Eyring's model (EM) for shear thinning are derived. It is argued that an "incremental viscosity," η i , or IV which is the derivative of the steady state stress with respect to the shear rate is a better measure of the physical state of the system than the conventional definition of the shear rate dependent viscosity (i.e., the shear stress divided by the strain rate). The stress relaxation function, C i (t), associated with η i is consistent with Boltzmann's superposition principle and is computed by NEMD and the EM. The IV of the Eyring model is shown to be a special case of the Carreau formula for shear thinning. An analytic solution for the transient time correlation function for the EM is derived. An extension of the EM to allow for significant local shear stress fluctuations on a molecular level, represented by a gaussian distribution, is shown to have the same analytic form as the original EM but with the EM stress replaced by its time and spatial average. Even at high shear rates and on small scales, the probability distribution function is almost gaussian (apart from in the wings) with the peak shifted by the shear. The Eyring formula approximately satisfies the Fluctuation Theorem, which may in part explain its success in representing the shear thinning curves of a wide range of different types of chemical systems.

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“…Using non-classical information theory based on Bose-Einstein statistics, i.e. assuming that the individual contributions to I(co) at a given co are not distinguishable, Powles and Carazza [14] predicted, using as an input the second moment, lorentzian like co-z decay at the wings. Obviously the addition of more moments as input will result in a faster decay again inconsistent with the co-4 behaviour.…”

Section: Discussionmentioning

confidence: 99%