Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble
Abstract
We study the thermodynamic and statistical properties of a gas governed by a multifractional modified dispersion relation of the form ω2=k2+4E*−1/2k5/2, where E* sets the characteristic scale of the multifractional correction. Working within the grand-canonical ensemble, we derive the modified density of states, the grand potential, the partition function, and the main thermodynamic quantities for both bosonic and fermionic sectors. The deformation changes the available phase-space distribution and produces nonstandard thermal scalings controlled by the ratio T/E*. In the infrared regime, the usual relativistic gas behavior is recovered with leading corrections proportional to powers of (T/E*)1/2. In the ultraviolet regime, the density of states scales as ϱ(ω)∝ ω7/5, corresponding to an effective density-of-states dimension deff=12/5. As a consequence, the Stefan-Boltzmann law is deformed from u∝ T4 to u∝ E*3/5T17/5, while the equation-of-state parameter approaches w=5/12 instead of the standard radiation value w=1/3. We also analyze thermal stability, particle number and energy fluctuations, Bose-Einstein condensation, and the degenerate Fermi gas limit. The multifractional correction increases the critical temperature of a conserved bosonic gas and modifies the Fermi energy, pressure, sound speed, and low-temperature heat capacity of degenerate fermions. A direct fit to the COBE/FIRAS monopole spectrum yields E*>0.36 MeV at 95% CL, while the conservative GWTC--3 propagation constraint gives E*>1.18×1019 GeV at 90% credibility when the dispersion relation is assumed to be universal.
Related
- Dispersion relation, propagation features and canonical gauge structure of GNLED
- Thermodynamic topology of AdS black holes with FαβFγλRαγRβλ coupling in the grand canonical ensemble
- Thermodynamic and Statistical Signatures of Modality Changes in Concentration Distributions Driven by Stochastic Switching Between Two Activity States
- Structural, electronic, spectroscopic, and thermodynamic properties of gentisic acid: solvent and temperature effects using DFT and TD-DFT approaches
- Thermodynamic and structural properties of the thin atmosphere of a white dwarf
BibTeX
@misc{filho2026thermodynamic,
title = {{Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble}},
author = {A. A. Araújo Filho},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.16424},
eprint = {2605.16424},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.16424},
}
RIS
TY - UNPB
TI - Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble
AU - A. A. Araújo Filho
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2605.16424
UR - https://arxiv.org/abs/2605.16424
AB - We study the thermodynamic and statistical properties of a gas governed by a multifractional modified dispersion relation of the form ω^2=k^2+4E_*^−1/2k^5/2, where E_* sets the characteristic scale of the multifractional correction. Working within the grand-canonical ensemble, we derive the modified density of states, the grand potential, the partition function, and the main thermodynamic quantities for both bosonic and fermionic sectors. The deformation changes the available phase-space distribution and produces nonstandard thermal scalings controlled by the ratio T/E_*. In the infrared regime, the usual relativistic gas behavior is recovered with leading corrections proportional to powers of (T/E_*)^1/2. In the ultraviolet regime, the density of states scales as ϱ(ω)∝ ω^7/5, corresponding to an effective density-of-states dimension d_eff=12/5. As a consequence, the Stefan-Boltzmann law is deformed from u∝ T^4 to u∝ E_*^3/5T^17/5, while the equation-of-state parameter approaches w=5/12 instead of the standard radiation value w=1/3. We also analyze thermal stability, particle number and energy fluctuations, Bose-Einstein condensation, and the degenerate Fermi gas limit. The multifractional correction increases the critical temperature of a conserved bosonic gas and modifies the Fermi energy, pressure, sound speed, and low-temperature heat capacity of degenerate fermions. A direct fit to the COBE/FIRAS monopole spectrum yields E_*>0.36 MeV at 95% CL, while the conservative GWTC--3 propagation constraint gives E_*>1.18×10^19 GeV at 90% credibility when the dispersion relation is assumed to be universal.
ER -