scholarly journals On Boundedness of Entropy of Photon Gas in Noncommutative Spacetime

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Kazi Ashraful Alam ◽  
Mir Mehedi Faruk
Keyword(s):  
Black Holes ◽  
Distribution Function ◽  
Phase Space ◽  
Partition Function ◽  
Boltzmann Distribution ◽  
Einstein Distribution ◽  
Entropy Bound ◽  
Photon Gas ◽  
Noncommutative Spacetime ◽  
Bose Einstein

Entropy bound for the photon gas in a noncommutative (NC) spacetime where phase space is with compact spatial momentum space, previously studied by Nozari et al., has been reexamined with the correct distribution function. While Nozari et al. have employed Maxwell-Boltzmann distribution function to investigate thermodynamic properties of photon gas, we have employed the correct distribution function, that is, Bose-Einstein distribution function. No such entropy bound is observed if Bose-Einstein distribution is employed to solve the partition function. As a result, the reported analogy between thermodynamics of photon gas in such NC spacetime and Bekenstein-Hawking entropy of black holes should be disregarded.

Thermal Rectification by Ballistic Phonons

2008 ◽  
Author(s):  
John Miller ◽  
Wanyoung Jang ◽  
Chris Dames
Keyword(s):  
Distribution Function ◽  
Mean Free Path ◽  
Temperature Gradients ◽  
Reverse Direction ◽  
Large Temperature ◽  
Thermal Rectification ◽  
Einstein Distribution ◽  
Ballistic Phonons ◽  
Dimensional Electron Gas ◽  
Bose Einstein

In analogy to the asymmetric transport of electricity in a familiar electrical diode, a thermal rectifier transports heat more favorably in one direction than in the reverse direction. One approach to thermal rectification is asymmetric scattering of phonons and/or electrons, similar to suggestions in the literature for a sawtooth nanowire [1] or 2-dimensional electron gas with triangular scatterers [2]. To model the asymmetric heat transport in such nanostructures, we have used phonon ray-tracing, focusing on characteristic lengths that are small compared to the mean free path of phonons in bulk. To calculate the heat transfer we use a transmission-based (Landauer-Buttiker) method. The system geometry is described by a four-dimensional transfer function that depends on the position and angle of phonon emission and absorption from each of two contacts. At small temperature gradients, the phonon distribution function is very close to the usual isotropic equilibrium (Bose-Einstein) distribution, and there is no thermal rectification. In contrast, at large temperature gradients, the anisotropy in the phonon distribution function becomes significant, and the resulting heat flux vs. temperature curve (analogous to I-V curve of a diode) reveals large thermal rectification.

scholarly journals Maxwell–Boltzmann type Hawking radiation

2017 ◽  
Vol 32 (12) ◽  
pp. 1750071 ◽  
Author(s):  
Youngsub Yoon
Keyword(s):  
Black Hole ◽  
Hawking Radiation ◽  
Radiation Spectrum ◽  
Boltzmann Distribution ◽  
Black Hole Horizon ◽  
Not Given ◽  
Horizon Area ◽  
Einstein Distribution ◽  
Bose Einstein

Twenty years ago, Rovelli proposed that the degeneracy of black hole (i.e. the exponential of the Bekenstein–Hawking entropy) is given by the number of ways the black hole horizon area can be expressed as a sum of unit areas. However, when counting the sum, one should treat the area quanta on the black hole horizon as distinguishable. This distinguishability of area quanta is noted in Rovelli’s paper. Building on this idea, we derive that the Hawking radiation spectrum is not given by Planck radiation spectrum (i.e. Bose–Einstein distribution) but given by Maxwell–Boltzmann distribution.

scholarly journals Entropy bound for the photon gas in noncommutative spacetime

2016 ◽  
Vol 82 ◽  
pp. 66-71 ◽  
Author(s):  
K. Nozari ◽  
M.A. Gorji ◽  
A. Damavandi Kamali ◽  
B. Vakili
Keyword(s):  
Entropy Bound ◽  
Photon Gas ◽  
Noncommutative Spacetime

scholarly journals A Note on Effects of Generalized and Extended Uncertainty Principles on Jüttner Gas

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 213
Author(s):  
Hooman Moradpour ◽  
Sarah Aghababaei ◽  
Amir Hadi Ziaie
Keyword(s):  
Distribution Function ◽  
Partition Function ◽  
Energy Density ◽  
Thermal Energy ◽  
Boltzmann Distribution ◽  
High Energy ◽  
Uncertainty Principles ◽  
Relativistic Limit ◽  
Boltzmann Statistics ◽  
Extended Uncertainty

In recent years, the implications of the generalized (GUP) and extended (EUP) uncertainty principles on Maxwell–Boltzmann distribution have been widely investigated. However, at high energy regimes, the validity of Maxwell–Boltzmann statistics is under debate and instead, the Jüttner distribution is proposed as the distribution function in relativistic limit. Motivated by these considerations, in the present work, our aim is to study the effects of GUP and EUP on a system that obeys the Jüttner distribution. To achieve this goal, we address a method to get the distribution function by starting from the partition function and its relation with thermal energy which finally helps us in finding the corresponding energy density states.

scholarly journals Multiphase Simulated Annealing Based on Boltzmann and Bose-Einstein Distribution Applied to Protein Folding Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Juan Frausto-Solis ◽  
Ernesto Liñán-García ◽  
Juan Paulo Sánchez-Hernández ◽  
J. Javier González-Barbosa ◽  
Carlos González-Flores ◽  
...  
Keyword(s):  
Protein Folding ◽  
Simulated Annealing ◽  
Simulated Annealing Algorithm ◽  
Least Squares Method ◽  
Equilibrium Phase ◽  
Boltzmann Distribution ◽  
New Approach ◽  
Einstein Distribution ◽  
Problem Instances ◽  
Bose Einstein

A new hybrid Multiphase Simulated Annealing Algorithm using Boltzmann and Bose-Einstein distributions (MPSABBE) is proposed. MPSABBE was designed for solving the Protein Folding Problem (PFP) instances. This new approach has four phases: (i) Multiquenching Phase (MQP), (ii) Boltzmann Annealing Phase (BAP), (iii) Bose-Einstein Annealing Phase (BEAP), and (iv) Dynamical Equilibrium Phase (DEP). BAP and BEAP are simulated annealing searching procedures based on Boltzmann and Bose-Einstein distributions, respectively. DEP is also a simulated annealing search procedure, which is applied at the final temperature of the fourth phase, which can be seen as a second Bose-Einstein phase. MQP is a search process that ranges from extremely high to high temperatures, applying a very fast cooling process, and is not very restrictive to accept new solutions. However, BAP and BEAP range from high to low and from low to very low temperatures, respectively. They are more restrictive for accepting new solutions. DEP uses a particular heuristic to detect the stochastic equilibrium by applying a least squares method during its execution. MPSABBE parameters are tuned with an analytical method, which considers the maximal and minimal deterioration of problem instances. MPSABBE was tested with several instances of PFP, showing that the use of both distributions is better than using only the Boltzmann distribution on the classical SA.

A Broad Range of Phonon Mean Free Paths Is Important for Heat Conduction

2008 ◽  
Author(s):  
C. Dames
Keyword(s):  
Thermal Conductivity ◽  
Distribution Function ◽  
Heat Conduction ◽  
Mean Free Path ◽  
Angular Frequency ◽  
Boundary Scattering ◽  
Spectral Form ◽  
Einstein Distribution ◽  
K 13 ◽  
Bose Einstein

The thermal conductivity is modeled with a spectral form of kinetic theory k=13∫CωνLdω(1) where ω is the angular frequency, Cω is the specific heat per unit frequency, ν = ∂ω/∂q is the group velocity, and L is the effective mean free path (MFP) which combines bulk and boundary scattering using Matthiessen’s rule: Cω=ħωDOS∂f/∂T(2)L−1=Lbulk−1+Lboundary−1.(3) Here q is the wavevector, DOS is the density of states (acoustic modes only), T is the temperature, and f is the Bose-Einstein distribution function.

scholarly journals The statistical mechanics of near-extremal black holes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Luca V. Iliesiu ◽  
Gustavo J. Turiaci
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Partition Function ◽  
Gauge Field ◽  
Dimensional Reduction ◽  
Degrees Of Freedom ◽  
Energy Scale ◽  
Fixed Charge ◽  
Extremal Black Hole ◽  
Extremal Black Holes

Abstract An important open question in black hole thermodynamics is about the existence of a “mass gap” between an extremal black hole and the lightest near-extremal state within a sector of fixed charge. In this paper, we reliably compute the partition function of Reissner-Nordström near-extremal black holes at temperature scales comparable to the conjectured gap. We find that the density of states at fixed charge does not exhibit a gap; rather, at the expected gap energy scale, we see a continuum of states. We compute the partition function in the canonical and grand canonical ensembles, keeping track of all the fields appearing through a dimensional reduction on S2 in the near-horizon region. Our calculation shows that the relevant degrees of freedom at low temperatures are those of 2d Jackiw-Teitelboim gravity coupled to the electromagnetic U(1) gauge field and to an SO(3) gauge field generated by the dimensional reduction.

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