Long-time tail in an electric conduction system

Fluctuation theorem for irreversible entropy production in electrical conduction

Linear, irreversible thermodynamics predicts that the entropy production rate can become negative. We demonstrate this prediction for metals under AC-driving whose conductivity is well-described by the Drude-Sommerfeld model. We then show that these negative rates are fully compatible with stochastic thermodynamics, namely, that the entropy production does fulfill a fluctuation theorem. The analysis is concluded with the observation that the stochastic entropy production as defined by the surprisal or ignorance of the Shannon information does not agree with the phenomenological approach.

Fractal and Multifractal Scaling of Electrical Conduction in Random Resistor Networks

This article is a mini-review about electrical current flows in networks from the perspective of statistical physics. We briefly discuss analytical methods to solve the conductance of an arbitrary resistor network. We then turn to basic results related to percolation: namely, the conduction properties of a large random resistor network as the fraction of resistors is varied. We focus on how the conductance of such a network vanishes as the percolation threshold is approached from above. We also discuss the more microscopic current distribution within each resistor of a large network. At the pe…

DC electric field effect on the anomalous exponent of the hopping conduction in the one-dimensional disorder model

DC electric field effect on the anomalous exponent of the hopping conduction in the disorder model is investigated. First, we explain the model and derive an analytical expression of the effective waiting time for the general case. We show that the exponent depends on the external field. Then we focus on a one-dimensional system in order to illustrate the features of the anomalous exponent. We derive approximate expressions of the anomalous exponent of the system analytically. For the case of a weak field, the anomalous exponent is consistent with that of diffusive systems. This is consistent …

平面上曲线性物体随机系统中的渗流与导电：计算机模拟与平均场方法

Percolation and electrical conduction in random systems of curved linear objects on a plane: computer simulations along with a mean-field approach

该研究用圆弧模拟零宽度弯曲金属纳米线，结合 Monte Carlo 模拟与平均场近似，分析二维随机网络的渗流阈值及总电导，并揭示固定长度下形状由直棒变圆环时电导降低。