Transport Coefficients from Large Deviation Functions

Han

The Journal of Chemical Physics

et al. 2018

We study two types of intrinsic uncertainties, statistical errors and system size effects, in estimating shear viscosity via equilibrium molecular dynamics simulations, and compare them with the corresponding uncertainties in evaluating the self-diffusion coefficient. Uncertainty quantification formulas for the statistical errors in the shear-stress autocorrelation function and shear viscosity are obtained under the assumption that shear stress follows a Gaussian process. Analyses of simulation results for simple and complex fluids reveal that the Gaussianity is more pronounced in the shear-stress process (related to shear viscosity estimation) compared with the velocity process of an individual molecule (related to self-diffusion coefficient). At relatively high densities corresponding to a liquid state, we observe that the shear viscosity exhibits complex size-dependent behavior unless the system is larger than a certain length scale, and beyond which, reliable shear viscosity values are obtained without any noticeable scaling behavior with respect to the system size. We verify that this size-dependent behavior is configurational and relate the characteristic length scale to the shear-stress correlation length.

Section: Introductionmentioning

confidence: 99%

Nature of intrinsic uncertainties in equilibrium molecular dynamics estimation of shear viscosity for simple and complex fluids

Han

The Journal of Chemical Physics

et al. 2018

“…As the measured transport coefficients depend significantly on the exact individual nature of the sample; e.g., the grain size and boundaries [41,42]-care must be taken when using relations like Equation (3). To overcome these problems, the direct calculation of the conductivities can be done using MD [43][44][45]. We believe that the processes across the cell are the most relevant to give insights of the coupled mechanisms and, thus, we limit our study to the spatial dimension perpendicular to the cell area.…”

Section: Introductionmentioning

confidence: 99%

Impact of Multi-Causal Transport Mechanisms in an Electrolyte Supported Planar SOFC with (ZrO2)x−1(Y2O3)x Electrolyte

Huerta¹,

Flasbart²,

Marquardt³

et al. 2018

Entropy

The calculation of the entropy production rate within an operational high temperature solid oxide fuel cell (SOFC) is necessary to design and improve heating and cooling strategies. However, due to a lack of information, most of the studies are limited to empirical relations, which are not in line with the more general approach given by non-equilibrium thermodynamics (NET). The SOFC 1D-model presented in this study is based on non-equilibrium thermodynamics and we parameterize it with experimental data and data from molecular dynamics (MD). The validation of the model shows that it can effectively describe the behavior of a SOFC at 1300 K. Moreover, we show that the highest entropy production is present in the electrolyte and the catalyst layers, and that the Peltier heat transfer is considerable for the calculation of the heat flux in the electrolyte and cannot be neglected. To our knowledge, this is the first validated model of a SOFC based on non-equilibrium thermodynamics and this study can be extended to analyze SOFCs with other solid oxide electrolytes, with perovskites electrolytes or even other electrochemical systems like solid oxide electrolysis cells (SOECs).

The Journal of Chemical Physics

“…Each individual trajectory is known as a walker, and collectively they undergo a population dynamics that samples a biased trajectory ensemble. A more detailed description of the algorithm can be found in our earlier work [40].…”

Section: Numerical Evaluation Of Large Deviation Functionsmentioning

confidence: 99%

Nonlinear transport coefficients from large deviation functions

Gao

Limmer

2019

Nonlinear response occurs naturally when a strong perturbation takes a system far from equilibrium. Despite of its omnipresence in nanoscale systems, it is difficult to predict in a general and efficient way. Here we introduce a way to compute arbitrarily high order transport coefficients of stochastic systems, using the framework of large deviation theory. Leveraging time reversibility in the microscopic dynamics, we relate nonlinear response to equilibrium multi-time correlation functions among both time reversal symmetric and asymmetric observables, which can be evaluated from derivatives of large deviation functions. This connection establishes a thermodynamic-like relation for nonequilibrium response and provides a practical route to its evaluation, as large deviation functions are amenable to importance sampling. We demonstrate the generality and efficiency of this method in predicting transport coefficients in single particle systems and an interacting system exhibiting thermal rectification. arXiv:1812.01470v2 [cond-mat.stat-mech]