9k views

### Why do some substances undergo sublimation while others do not?

This question is indeed lengthy, but please go through the question at least. From the study of kinetic theory I know that for intuitive answers we can associate the states (liquid, solid,gas) with ...
• 452
2k views

### Extending the ergodic theorem to non-equilibrium systems

I try to make this as short and concise as possible. For equilibrium systems in statistical mechanics, we have the Liouville's theorem which says that the volume in phase space is conserved when the ...
• 4,655
2k views

• 2,661
786 views

### How does the fluctuation theorem dissipation function become entropy?

In "The Fluctuation Theorem" by Evans and Searles, they derive the transient fluctuation theorem from Liouville's theorem (pg 1541). Following their notation $\Gamma = (\vec{q}, \vec{p})$, they use ...
496 views

### How many temperatures has a plasma?

In nonthermal plasma, not all particles move in the same way. The electrons are different from other particles. Both can be described as having a temperature separately. But that would mean, one piece ...
• 3,901
974 views

### Gibbs entropy, Clausius' entropy and irreversibility

I have a bunch of doubts and confusions on the concept of entropy which have been bothering me for a while now. The most important ones are of a more technical nature, arisen from the reading of this ...
• 1,262
1 vote
2k views

### Mach Number after Normal Shock

Is there any way that someone can give me more of a conceptual explanation for the fact that the Mach number downstream of a normal shock must be less than or equal to 1? I understand the ...
624 views

### Current density in phase space

$\newcommand{\dd}{{\rm d}}$ I have a question which arises from looking at the impact free Boltzmann equation. Let $(\vec{x},\vec{v})$ be a vector in our phase space $\Gamma^N = \mathbb{R}^{6N}$. The ...
251 views

### Why does distribution density seem to change though Liouville says it shouldn't?

I am trying to get a deeper understanding of Liouville's theorem and the distribution function in general. As an aid, I was thinking of the following simple, one-dimensional case: ball bearings are ...
• 65
I look to solve analytically the Vlasov-Maxwell equations for a magnetized hot plasma \frac{\partial f_{s1}}{\partial t}+\vec{v}\cdot\frac{\partial f_{s1}}{\partial \vec{r}}+\frac{q_s}{m_s}\Big(\vec{...