$q$-deformed Einstein's Model to Describe Specific Heat of Solid

TL;DR

This paper generalizes Einstein's model for specific heat of solids using Tsallis statistics, introducing a fluctuation parameter q, which accurately fits experimental data and aligns with Debye's theory, especially at low temperatures.

Contribution

The authors develop a q-deformed Einstein model within Tsallis statistics, incorporating temperature fluctuations to better match experimental specific heat data and connect with Debye's theory.

Findings

q-deformed Einstein curve fits experimental data at low temperatures

The model reproduces Debye's results with a temperature-dependent q

A single Einstein temperature and q(T) describe specific heat phenomena

Abstract

Realistic phenomena can be described more appropriately using generalized canonical ensemble, with proper parameter sets involved. We have generalized the Einstein's theory for specific heat of solid in Tsallis statistics, where the temperature fluctuation is introduced into the theory via the fluctuation parameter $q$. At low temperature the Einstein's curve of the specific heat in the nonextensive Tsallis scenario exactly lies on the experimental data points. Consequently this $q$-modified Einstein's curve is found to be overlapping with the one predicted by Debye. Considering only the temperature fluctuation effect(even without considering more than one mode of vibration is being triggered) we found that the $C_V$ vs $T$ curve is as good as obtained by considering the different modes of vibration as suggested by Debye. Generalizing the Einstein's theory in Tsallis statistics we found that a unique value of the Einstein temperature $\theta_E$ along with a temperature dependent deformation parameter $q(T)$, can well describe the phenomena of specific heat of solid i.e. the theory is equivalent to Debye's theory with a temperature dependent $\theta_D$.