0
votes
0answers
27 views

Section of Phase space

Suppose $\mathfrak{X}$ is the configuration space of some system on a Riemannian manifold $\mathcal{M}$. Then, the phase space is $\mathrm{T}^{*}(\mathfrak{X})$. What is a section of ...
7
votes
3answers
292 views

Is particle number a problem for formulating statistical physics in a mathematically rigorous manner?

Quantities like the chemical potential can be expressed as something like $$\mu=-T\left(\tfrac{\partial S}{\partial N}\right)_{E,V}.$$ Now the entropy is the log some volume, which depends on the ...
1
vote
0answers
187 views

What does it mean for a phase space trajectory to be “long” and “stable”?

What does it mean for a phase space trajectory to be "long" and "stable"? I understand the concept of a trajectory in phase space but not how these adjectives can be applied to one. Thanks.