Questions tagged [statistical-mechanics]
The study of large, complicated systems employing statistics and probability theory to extract average properties and to provide a connection between mechanics and thermodynamics.
7,308 questions
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Ideal gas equation [closed]
While deriving ideal gas equation we assumed the container to be a cuboid and then we took the volume to be $lbh$ where l, b, h are length, breadth, and height respectively. Will the equation still be ...
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1 vote
1 answer
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Phase transition for first moments in the 2D random-bond Ising model
I have a very basic confusion about the 2D random-bond Ising model on a square lattice with Boltzmann weight $$\omega(J_{ij},\sigma_j)=\prod_{ij}(1-p)^{\delta_{J_{ij}=1}} p^{\delta_{J_{ij}=-1}} e^{-\...
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1 answer
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Cooling molecules with photons
Let's say there is a group of molecules confined in a box. Because of the molecules, the temperature in the box reaches up to 5000 kelvin. Each molecule in the box has about 1.036 * 10^-19 Joules (...
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What is level of the energy and what is state in a box? [closed]
I am currently studying statistical mechanics and I figure I do not understand what is energy level and state, by learning the concept of density of state. When we think about placing N particles ...
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Maxwell-Juttner distribution and its derivation
I am looking for good notes on the Maxwell-Juttner distribution and its derivation. I stumbled across this post Calculation of Maxwell-Juttner distribution integral but I was unable to find reference ...
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1 vote
2 answers
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What is the mechanism behind the Curie point in ferromagnets?
I just finished up a uni course on magnetism, which mostly made sense, but I've been left with some questions about ferromagnetic behaviour; in particular, I'm not satisfied with my lecturer's ...
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1 answer
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What causes the difference in the graphs showing the dependence of a molecule's potential energy on distance?
"The potential curve will have the shape shown in the figure above if the molecules approach each other in plane A along the line connecting their centers". "If the molecules approach ...
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-2 votes
1 answer
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Can ideal gasses achieve negative temperature? [closed]
I wish to know if ideal gasses can achieve negative temperatures and if it has been experimentally achieved in some form or not. The reason I am interested in this is because, for ideal gasses we have ...
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2 votes
1 answer
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What does grand potential for $2D$ systems mean?
In $3D$ the grand potential $\Omega = -PV$ has a well-defined physical meaning. But for $2D$ systems what would $\Omega$ actually mean physically? Dimensionally speaking it looks like $\Omega = -\...
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2 votes
2 answers
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How to see entropy vanishes for fermionic gas at $T = 0$ from the grand potential?
I want to see the entropy of a Fermi gas vanish at $T=0$ without using the density matrix as some answers have utilized online. The grand potential for fermi gas (Second Eq. in Sec. 9.4 on page 92) is ...
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3 votes
0 answers
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Diffusion equation after one time-step [closed]
Consider the equation: $$ \partial_tu=D\partial_{xx}^2u $$ with reflecting boundary condition at $x=0$ and with $u(x,0)=\delta(x)$ as an initial distribution. First question: How should I understand a ...
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2 votes
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How does Energy Enter Chemical Potential?
Energy should enter the chemical potential as: $$\mu N = U - TS + pV\;,$$ that is, with a positive sign. That means that if I add a potential (energy per particle) of $\phi$, then the energy should ...
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1 vote
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Kolmogorov complexity in physics - applications [duplicate]
Has there been application of Kolmogorov complexity to physics? Shannon entropy has an interpretation from thermodynamics. In principle Kolmogorov complexity and Shannon entropy are the same but is ...
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3 votes
2 answers
134 views
Pressure of thermal system at equilibrium
This question may sound stupid. Consider a system at equilibrium. If we use the canonical ensemble, then the pressure of the system is(if I'm right) $$p=-\sum_s {p_s \frac{\mathbb d E_s}{\mathbb d V}},...
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2 votes
1 answer
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Alternate statement for Liouville's theorem: Can you say that the relative velocity between any two representative points is zero?
So Liouville's theorem basically says the local density of representative points stays constant or that the flow of representative points resembles that of an incompressible fluid. Can you then say ...
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