English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this letter, we present the unified paradigm on entropy-ruled Einsteindiffusion-mobility relation ({\mu}/D ratio) for all dimensional systems (1D, 2Dand 3D) of molecules and materials. The different dimension-associatedfractional value of the variation in differential entropy with respect to thechemical potential ({\Delta}h/{\Delta}{\eta}) gives the quantum-classicaltransition version of {\mu}/D relation. This is a new alternative version forquantum devices, instead of Einstein original relation of {\mu}/D = q/kT; whereq, k and T are the electric charge, Boltzmann constant and temperature,respectively. It is found that the fractional value of {\Delta}h/{\Delta}{\eta}for {\mu}/D ratio for different dimensional systems or devices is a directconsequences with the average energy-Fermi energy relation, which can varieswith the typical dimensions, whether the system belongs to 1D or 2D or 3D. Thisunified entropy-ruled transport formalism works well for both the quantum andclassical systems with equilibrium as well as non-equilibrium conditions. Basedon the dimensional dependent entropy-ruled {\mu}/D factor, theNavamani-Shockley diode equation is transformed.

Unified Entropy-Ruled Einstein Relation for Bulk and Low-Dimensional Systems: A Hopping to Band Shift Analysis