All Questions
Tagged with cosmology statistical-mechanics
77
questions
0
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67
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Why can we use Bose-Einstein statistics in this expression for number density
In a system with $N$ particles in some volume $V$ in contact with a reservoir of temperature $T$, we find that
$$\bar{n_i}=\frac{g_i}{e^{\frac{{\epsilon}_i -\mu}{kT}} \pm 1}$$
depending on whether the ...
- 91
1
vote
2
answers
180
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Kolb and Turner's expresion for number density Eqn. (3.46) and pressure in Eqn. (3.48)
Having defined the phase space distribution function $f(\textbf{r},\textbf{p},t)$ in $\mu-$space, one can express the information that there are $N$ particles in the volume $V$ through the condition \...
- 11
5
votes
1
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Net particle number density for relativistic particles at finite chemical potential (tricky integral)
Question: How does one show that the chemical potential of relativistic fermions is negligible at high energies? In particular, I would like to show that the difference between the particle density $n$...
- 13.1k
4
votes
2
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139
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Why can photon be treated like gas?
In Cosmology, especially when studying Cosmic Dynamic, sometime we will treat photons as gas to calculate its pressure, but according to my understanding, photon and gas are nothing alike. Why can ...
- 4,954
2
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5
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A few questions about Boltzmann brains [closed]
So I've been thinking about Boltzmann brains and there are some questions which I wasn't able to answer online:
Given that Boltzmann brains only last for a split second, is experience (the notion or ...
- 6,217
2
votes
1
answer
195
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Determining free Fermi/Bose gas chemical potentials, given temperature, number density, and baryon density
I'm attempting to recreate some plots of individual particle chemical potentials from S. Reddy et. al.'s paper on neutrino interactions in hot and dense matter (of the same title). The specifics aren'...
- 18.8k
2
votes
2
answers
286
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Why can't primordial fluctuations be super-"horizon" without inflation?
I am trying to understand why, in cosmology, it is said that the presence of fluctuations at scales above the Hubble distance would not be expected in the absence of inflation or something like it.
We ...
- 6,501
60
votes
9
answers
8k
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How do different definitions of entropy connect with each other?
In many places over the Internet, I have tried to understand entropy.
Many definitions are presented, among which I can formulate three (please correct me if any definition is wrong):
Entropy = ...
- 181
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votes
0
answers
32
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Poincaré recurrence in a closed universe? [duplicate]
Is it possible that the Poincaré recurrence applies to a closed universe (with a finite spacetime)? If it is, would this mean that a closed universe could eventually reach the same state as its ...
- 2,472
8
votes
2
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3k
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Do Boltzmann brain thought experiments suggest literally anything can form randomly?
Do Boltzmann brain thought experiments suggest literally anything can form randomly?
What are the limitations to what random fluctuations can form? Literally any physical, material object?
Lastly, I ...
- 2,550
0
votes
1
answer
64
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Integral on the solid angle of a function of the direction [closed]
I need to compute the integral
$$\int \frac{d^3q}{(2\pi)^3} \frac{q}{E}n^in^jn^k \frac{\partial g}{\partial x^i}$$
where $n^i$, $n^j$ and $n^k$ are the unit vectors and $g$ is a function of the ...
- 21.9k
15
votes
4
answers
3k
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If dark matter can't lose kinetic energy, then why is it not traveling at relativistic speeds?
I have read this question:
The only way you can do this is to remove kinetic energy from the system.
With normal matter this is done through electromagnetic interactions, which turn the kinetic ...
- 27.5k
1
vote
1
answer
94
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The content of early universe and max limit on the number of particles
When the size of the observable universe was small as a proton what was the physical content of it?
Was there a limit of particles in such a tiny volume with enormous high density and energy?
Can we ...
- 489
5
votes
3
answers
925
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Why does the CMB have a spectrum like a black-body radiation?
Equilibrium distributions of particles (Maxwell, Boltzmann, Saha) are achieved by the particle collisions. On the other hand, photons do not interact with each other. From the introductory course in ...
- 133k
9
votes
4
answers
4k
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Is heat death reversible by thermal or quantum fluctuations given an infinite time?
I'm new here, so apologies if the question doesn't sound meaningful considering what physics is supposed to answer. I don't have a physics or mathematics background, but I did learn a few things about ...
- 207k