All Questions
Tagged with classical-mechanics statistical-mechanics
189
questions
-1
votes
2
answers
487
views
What are some examples of microscopic quantities?
Mass, volume, energy, entropy, temperature, pressure are some macroscopic quantities. Which means we can think of them even without considering the molecular nature of matter.
What are some examples ...
- 521
1
vote
0
answers
85
views
Equipartition theorem for continous medium
The equipartition theorem states that if $x_i$ is a canonical variable (either position or momentum), then
$$\left\langle x_i \frac{\partial \mathcal{H}}{\partial x_j}\right\rangle = \delta_{ij}\ k T.$...
- 133
0
votes
1
answer
184
views
Integration by Parts in Liouville's Theorem
I am looking at a proof of Liouville's Theorem, which states that for $F, G \in C_0^\infty$ and a Hamiltonian $H$, the operator
$$D_H = \sum_{i=1}^n\Big(\frac{\partial H}{\partial p_i} \frac{\partial}{...
- 3,350
0
votes
1
answer
59
views
What quantity can a microstate have? [closed]
I confused whether a microstate's chemistry potential is defined.
And how about temperature, pressure, entropy?
And what is a microstate? A ensemble contain a set of microstates. The microstate is a ...
- 11
4
votes
1
answer
229
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Liouville's Theorem & Flows in Phase Space for Particle in a Box
A Hamiltonian system of $100$ interacting oxygen atoms, each of mass $16$
$m_p$, is confined within a cubical box of sides $1 m$. The average initial
speed of each particle is $300 ms^{-1}$. Estimate ...
- 545
1
vote
0
answers
34
views
How to Calculate the average tension due to thermal fluctuations (past exam question)
I'm studying for an exam and this is a stat mech question from an old test:
I feel like there might be a typo but I'm not sure, and want to make sure I'm not doing anything wrong. This is what I've ...
- 63
0
votes
1
answer
40
views
Expected energy in micro-canonical and canonical distribution
Which relation $E(β)$ is required to ensure that he micro-canonical distribution and the canonical
distribution have the same expected energy?
- 23
1
vote
0
answers
47
views
Semi new approach to analyzing mechanical systems
In attempt to Analyze mechanical systems we have base our entire set of theorems on one principle which is very similar to the principle of stationary action:
“ System always evolves in a way that it ...
1
vote
1
answer
55
views
Using abrasive lapping, is it possible to make a perfectly round cylinder starting with imperfect cylinder(s)?
Centerless cylindrical lapping is a technique used to create a smooth and round cylinder through the use of microscopic abrasive compounds.
My question is a chicken and egg problem, because it seems ...
- 611
1
vote
0
answers
60
views
Does the Legendre transformation describe two views on the same physical system or different physical systems?
In mechanics we perform the Legendre transform to go from the Lagrangian $L(q, \dot{q})$ to the Hamiltonian $H(q, p)$. This seems to be describing the same physical system. $L$ and $H$ both describe ...
- 131
2
votes
0
answers
44
views
How are conjugate variables in mechanics and stat mech related to duality in convex optimization?
I recently studied duality in optimization where a primal optimization problem can be casted as a dual problem which provides meaningful lower bounds on the primal. There is also a notion of conjugate ...
- 131
3
votes
2
answers
1k
views
Very briefly, what is the relation/difference between classical field theory and classical thermodynamics/statistical mechanics?
This is probably not a good question, since I am at a fairly low level, but I am a little bit confused when the two concepts were described to me and it's bringing discomfort during my study.
What I ...
- 243
-3
votes
3
answers
197
views
Does the phase space exist in reality? [closed]
The concept of phase space really bothers me sometimes and the term is used across many branches of physics such as statistical mechanics, classical mechanics as well as in quantum mechanics. Does ...
- 21
4
votes
0
answers
63
views
How negligible is a term in the internal energy for the equipartion theorem in classical mechanics?
The equipartition theorem is a well-known result of classical statistical mechanics, and it states that if the Hamiltonian of a system can be written like this:
$$H=\sum_{j=1}^m {\alpha_j\ {x_j}^2}$$
...
- 41
0
votes
1
answer
55
views
Elastic Collision Point Masses / Hard Spheres:: Proof that Magnitude of Relative Velocity is Unchanged
Statement of the Problem
On our way to the Boltzmann Collision integral, we consider the perfectly elastic collision of two point-masses with identical mass. The velocities prior collision are denoted ...
- 103