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Published on: May 27, 2020
Unified Entropy-Ruled Einstein's Relation for Bulk and Low-Dimensional Molecular-Material Systems: A Hopping-to-Band
1Department of Physics, Centre for Research and Development (CFRD), KPR Institute of Engineering and Technology, Coimbatore-641407, India.
Abstract:
We present a unified paradigm on entropy-ruled Einstein's diffusion-mobility relation (μ/D ratio) for 1D, 2D, and 3D free-electron solid state systems. The localization transport in the extended molecules is well approximated by the continuum time-delayed hopping factor within our unified entropy-ruled transport method of noninteracting quantum systems. Moreover, we generalize an entropy-dependent diffusion relation for 1D, 2D, and 3D systems as defined by , where h and d are the effective entropy and dimension (d = 1, 2, 3), respectively. This generalized relation is valid for both equilibrium and nonequilibrium transport systems since the parameter h is closely connected with the nonequilibrium fluctuation theorem-based entropy production rule. Importantly, we herein revisit the Boltzmann approach using an entropy-ruled method for mobility calculation for the universal quantum materials that is expressed as , where is the diffusion constant for band transport systems and η is the chemical potential. According to our entropy-ruled μ/D relation, the Navamani-Shockley diode equation is transformed.
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