16
votes
Accepted
Does Poincare recurrence show that Gibbs entropy is not strictly increasing?
Your perplexity and observations about Huang's statement are well-founded. Indeed, Huang acritically repeats Zermelo's and Poincaré's arguments against Boltzmann's ideas.
One flaw in using the ...
8
votes
Accepted
Pressure of a gas on the inside walls of a cylinder canonical ensemble
That's a good question. Which is similar to the (more common) question: "What's the pressure of a gas in a gravitational field" (for which you will be able to find more information). The ...
- 1,508
8
votes
Accepted
Spin-Spin Correlation Function
Since
$$
M^2
=
\biggl( \sum_{i} s_i \biggr)^2
=
\biggl( \sum_{i} s_i \biggr)\biggl( \sum_{j} s_j \biggr)
=
\sum_{i,j} s_i s_j,
$$
and
$$
\langle M\rangle^2
=
\biggl( \sum_{i} \langle s_i\rangle \biggr)...
- 10.6k
4
votes
Accepted
Radial distribution of ideal gas in a cylinder
Let's make it simpler. You have particle on a 2d plane with an Hamiltonian that depends on the distance to some center $r$ and also to the angle with respect to this center $\theta$. You can imagine ...
- 1,508
4
votes
How can events on the quantum-level be random but not on the macro-level?
All models are wrong; some are useful
"How science is explained" is really a topic for the math & science educators stack exchange. But if you want to look at what scientists really ...
- 50.7k
2
votes
Why do systems with greater energy fluctuation have better heat dissipation ability?
Your interpretation is on the right track. Larger fluctuations contribute to better dissipation for several reasons:
Why do larger fluctuations in equilibrium systems contribute to better dissipation ...
- 309
2
votes
Does Poincare recurrence show that Gibbs entropy is not strictly increasing?
Intuitively, one starts with a macro state and a corresponding micro state, eventually that micro state is arbitrarily close the original one, so the entropy should be get closer to the original value,...
- 61.8k
1
vote
Why do conserved quantities vanish when integrated against the collision integral?
I'm not completely sure I got your concern.
There might be two questions:
Why is this integral equal to 0?
It is 0 by definition of a collisional invariant. If we define:
$$\langle A\rangle(r, t)\...
- 1,508
1
vote
Does entropy outside of thermodynamics also increase?
You're trying to answer, the rate of change in entropy. Therefore, it is convenient to consider Stochastic processes, with time-dependent probability densities.
Now, for Markov processes, which have ...
- 3,111
1
vote
How can events on the quantum-level be random but not on the macro-level?
Central Limit Theorem and the thermodynamic limit provide that if a variable $X$ has a certain distribution, as you take the mean of $N$ instances of the variable (energy, momentum, etc), as $N$ gets ...
- 10.1k
1
vote
Can diffusion create a vacuum?
I have actually done this very experiment, starting with a sealed, permeable vessel (Teflon) filled with helium at 1 atm surrounded by air at 1 atm. What happens is over several days the pressure ...
- 10.1k
1
vote
Why is entropy's definition useful?
One thing entropy is NOT is a measure of energy dispersal. This erroneous idea is dangerously attractive because it is easy to understand and is sometimes true, but it leads to mistakes and should ...
- 3,168
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