1
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0answers
27 views

What is the fluctuations of the energy of a simple harmonic oscillator? [closed]

$$\begin{align} \varepsilon&=\frac{\vec{p}^{\,2}}{2m}+\frac{K}{m}\vec{q}^{\,2}\\ \rho(q,p)&=\biggl(\frac{\omega}{2\pi k_BT}\biggr)^3e^{-\frac{\varepsilon}{k_bT}} \end{align}$$ where ...
0
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1answer
46 views

What's wrong with this simple derivation of energy flux in a photon gas?

In a photon gas, we know that pressure, $P$, and energy density, $u$, are related by: $$P=\frac{u}{3}$$ We also know from relativity that the momentum of a photon is $$p=\frac{E}{c}$$ Finally, the ...
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0answers
21 views

What is Fermi energy and Fermi level? [duplicate]

What is meant by Fermi level and Fermi energy? And what is the difference between the two?
1
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0answers
107 views

Free Energy of N Spin 3/2 Particles

This question is from the book "Introductory Statistical Mechanics" by Bowley and Sanchez. The question is as follows: Calculate the free energy of a system with N particles, each with spin 3/2 with ...
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votes
2answers
101 views

Probability of having energy $E$ when $E$ is bounded

For a canonical ensemble the probability of a system to have energy $E$ is $P(E)=e^{-\beta E}$. For that we consider the that the system can have any energy between $0$ to $\infty$. What will be the ...
1
vote
3answers
406 views

What is the energy of a standing EM wave? Is it probabilistic?

In a cavity, the standing wave will constructively interfere with itself, so its energy gets higher while the oscillator is still vibrating. Since the vibration time is not a constant value, and ...
1
vote
2answers
517 views

Energy dependent Maxwell-Boltzmann distribution

I'm having a bit of a problem figuring out the energy dependent Maxwell-Boltzmann distribution. According to my book (Ashcroft & Mermin) they write the velocity dependent distribution as: ...
2
votes
2answers
85 views

What is the derivation for the exponential energy relation and where does it apply?

Very often when people state a relaxation time $\tau_\text{kin-kin}, \tau_\text{rot-kin}$,, etc. they think of a context where the energy relaxation goes as $\propto\text e^{-t/\tau}$. Related is an ...
1
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4answers
360 views

The Preference for Low Energy States

The idea that systems will achieve the lowest energy state they can because they are more "stable" is clear enough. My question is, what causes this tendency? I've researched the question and been ...
1
vote
1answer
180 views

Basic energy calculation for N identical spin system

We have a system that has N identical spins $n_i$, and each spin can be in state 1 or 0. The overall energy for the system is $\epsilon\sum_{i=1}^{N}n_i$. My understanding: There is only one ...
1
vote
2answers
318 views

Energy of particle in electric field

I'm taking a physics class and the professor teaches us really basic things in lecture and then gives homework way beyond what he taught in lecture. Obviously I need to find some resource other than ...
2
votes
1answer
1k views

Calculating partition function of ultra-relativistic 1D gas

This is a problem (Problem 3.16) from the book Statistical Mechanics 2nd Ed. by Pathria. In the problem I have to calculate the partition function of an ultra-relativistic 1D gas ($E_i=cp_i$) ...
1
vote
2answers
406 views

Maxwell-Boltzmann distribution and total energy per unit volume

We know that $$n(E) ~=~ \frac {2 \pi (N/V)}{(\pi k_B T)^{3/2}} E^{1/2} e^{-E/(k_B T)} dE,$$ where $V$ is total volume. If then, how do we derive total energy per unit volume from this equation?
1
vote
1answer
128 views

Where is the critical moment where the microcanonical ensemble enters the justification for the equilibium state?

As explained in many books, for the microscopic justification of the second law of thermodynamics (lets formulate it as the total entropy takes maximum among all possible exchanges of two systems), ...
7
votes
4answers
247 views

Is energy extensivity necessary in thermodynamics?

Given a partition of a system into two smaller systems, the energy $U$ is devided into $U_1$ and $U_2$, with $$U=\mathcal{P}(U_1,U_2):=U_1+U_2,$$ so that $U_2$ is given by $U-U_1$. Here the ...
6
votes
2answers
3k views

What is the relationship between Energy, Entropy, and Information?

What is the relationship between Energy, Entropy, and Information? I read this - What Is Energy? Where did it come from? - and the top answer says that 'energy' is an abstract number that is a ...
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1answer
592 views

Derivation of relativistic energy

The concept of relativistic energy comes from it's conservation in relativistic mechanics for an elastic collision. It seems to me that another possible derivation could equate the energy of a single ...
8
votes
2answers
396 views

Shaking a jar of balls

A jar is filled with two types of balls, red and green. Red balls have radius $r_1$ and mass $m_1$, green balls have radius $r_2$ and mass $m_2$. If initially the balls are randomly placed throughout ...
6
votes
3answers
1k views

Maxwell's Demon Constant (Information-Energy equivalence)

New Scientist article: Summon a 'demon' to turn information into energy The speed of light c converts between space and time and also appears in e=mc^2. Maxwell's Demon can turn information supplied ...