Difference between statistical and dynamical properties

[junt]

Hi All,

What are the main differences between statistical and dynamics properties in physics? Could you please explain the difference for problems in both classical and quantum mechanics. For instance, path integral molecular dynamics is supposed to give statistical properties of a quantum mechanical system. Can I say, time-dependent Schrödinger's equation gives the dynamical properties of a quantum mechanical system? What other examples of approaches can you give me to look for statistical and dynamical properties of a physical system?

Thanks!

 

[mikeyork]

I look at it this way:

The dynamics is described by (is additive in) the amplitude, the statistics by the relative frequency. Born's rule says they are connected since the latter is the square modulus of the former. So the dynamics determines the statistics but the reverse is not true.

 

[Jilang]

I look at it this way:

The dynamics is described by (is additive in) the amplitude, the statistics by the relative frequency. Born's rule says they are connected since the latter is the square modulus of the former. So the dynamics determines the statistics but the reverse is not true.

Why is the reverse not true?

 

[mikeyork]

Because the dynamics of multiple additive terms is lost.

 

[PeterDonis]

What are the main differences between statistical and dynamics properties in physics?

This question is way too general. Can you give some specific examples of properties in each category?