Between classical or quantum statistics

[GotTrips]

Hi can someone please help me! Can someone explain when it is acceptable to quantum statistics instead of classical statistics? And what is the difference between them.

Thanks All

OLY

 

[infra]

I don't remember the eqn but the critical word is "thermal wave length" that describes the difference between two. Look at th Huang's Statistical Mechenics for details

 

[dextercioby]

Microscopical dynamics and the application of the 6 postulates of (nonrelativistic) QM is the decisive factor...

Think of the Gibbs' paradox and u'll understand the need for a quantum statistical physics...


Daniel.

 

[seratend]

Microscopical dynamics and the application of the 6 postulates of (nonrelativistic) QM is the decisive factor...

Think of the Gibbs' paradox and u'll understand the need for a quantum statistical physics...

Daniel.

Not so easy. Please look at http://bayes.wustl.edu/etj/articles/gibbs.paradox.pdf

Seratend.

 

[dextercioby]

The Gibbs paradox is accounted for quite nicely even in classical statistic if one considers the dimensionless volume element on the phase space

$$d^{2s}\tilde{x}=:\frac{1}{h^{2s}}\prod_{i=1}^{2s} dq_{i}dp_{i}$$

to which the VI-th postulate is applied to

$$d^{2x}x^{*}=:\frac{1}{h^{2s}N!}\prod_{i=1}^{2s} dq_{i}dp_{i}$$

Daniel.