scholarly journals On the applicability of the equipartition theorem

2010 ◽  
Vol 14 (3) ◽  
pp. 855-858 ◽  
Author(s):  
Edward Bormashenko ◽  
Oleg Gendelman
Keyword(s):  
High Temperature ◽  
Low Temperatures ◽  
Standard Form ◽  
Temperature Limit ◽  
Large Displacements ◽  
Temperature Range ◽  
High Temperature Limit ◽  
Equipartition Theorem ◽  
Equipartition Of Energy

Generalization of the equipartition theorem is presented for a broad range of potentials U(x) with quadratic minimum. It is shown, that the equipartition of energy in its standard form appears at the low temperatures limit. For potentials demonstrating the quadratic behavior for large displacements from the equilibrium the equipartition holds also in the high temperature limit. The temperature range of applicability of the equipartition theorem for the potential U = ax2 + bx4 was established.

THERMODYNAMICS OF A WEAKLY DEFORMED CRYSTAL LATTICE WITH q-COMPLEX PARAMETER

1995 ◽  
Vol 09 (23) ◽  
pp. 1521-1525 ◽  
Author(s):  
L. DE FALCO ◽  
R. MIGNANI
Keyword(s):  
High Temperature ◽  
Low Temperatures ◽  
Deformation Parameter ◽  
Nonlinear Effects ◽  
Temperature Limit ◽  
Debye Model ◽  
Harmonic Oscillators ◽  
Complex Deformation ◽  
High Temperature Limit ◽  
External Perturbations

We use a system of deformed harmonic oscillators with complex deformation parameter to describe, by means of a q-deformed analogous to the Debye model, a solid subjected to external perturbations or with some nonlinear effects inside the lattice. In the case of a weak deformation, the specific heat of the lattice exhibits a departure from the standard behavior only at low temperatures, whereas the usual Dulong–Petit law is recovered in the high-temperature limit.

scholarly journals A 4d $$ \mathcal{N} $$ = 1 Cardy Formula

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Joonho Kim ◽  
Seok Kim ◽  
Jaewon Song
Keyword(s):  
Black Holes ◽  
Free Energy ◽  
Asymptotic Behavior ◽  
High Temperature ◽  
Gauge Theory ◽  
Chemical Potential ◽  
Temperature Limit ◽  
Superconformal Index ◽  
High Temperature Limit ◽  
Cardy Formula

Abstract We study the asymptotic behavior of the (modified) superconformal index for 4d $$ \mathcal{N} $$ N = 1 gauge theory. By considering complexified chemical potential, we find that the ‘high-temperature limit’ of the index can be written in terms of the conformal anomalies 3c − 2a. We also find macroscopic entropy from our asymptotic free energy when the Hofman-Maldacena bound 1/2 < a/c < 3/2 for the interacting SCFT is satisfied. We study $$ \mathcal{N} $$ N = 1 theories that are dual to AdS5 × Yp,p and find that the Cardy limit of our index accounts for the Bekenstein-Hawking entropy of large black holes.

scholarly journals Equations of viscous flow of silicate liquids with different approaches for universality of high temperature viscosity limit

2014 ◽  
Vol 8 (2) ◽  
pp. 59-68
Author(s):  
Ana Kozmidis-Petrovic
Keyword(s):  
High Temperature ◽  
Viscous Flow ◽  
Temperature Limit ◽  
High Temperature Limit ◽  
Viscosity Parameter ◽  
General Rules ◽  
Viscosity Limit ◽  
Dependent Parameter ◽  
Silicate Liquids ◽  
The Difference

The Vogel-Fulcher-Tammann (VFT), Avramov and Milchev (AM) as well as Mauro, Yue, Ellison, Gupta and Allan (MYEGA) functions of viscous flow are analysed when the compositionally independent high temperature viscosity limit is introduced instead of the compositionally dependent parameter ??. Two different approaches are adopted. In the first approach, it is assumed that each model should have its own (average) hightemperature viscosity parameter ??. In that case, ?? is different for each of these three models. In the second approach, it is assumed that the high-temperature viscosity is a truly universal value, independent of the model. In this case, the parameter ?? would be the same and would have the same value: log ?? = ?1.93 dPa?s for all three models. 3D diagrams can successfully predict the difference in behaviour of viscous functions when average or universal high temperature limit is applied in calculations. The values of the AM functions depend, to a greater extent, on whether the average or the universal value for ?? is used which is not the case with the VFT model. Our tests and values of standard error of estimate (SEE) show that there are no general rules whether the average or universal high temperature viscosity limit should be applied to get the best agreement with the experimental functions.

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