What is the comparison between the Born rule and thermodynamics?

[stevendaryl]

Consider a physical system in which the average value of position is $<x>=0$. What is the probability that the position is $x=1$ nm?

But if you also know $\langle x^2 \rangle, \langle x^3 \rangle, ...$?

 

[Blue Scallop]

I think such a question can be meaningfully asked only by using mathematical equations.

Ok, mathematically.. if we remove the position basis.. then there would be no decoherence and no subsystems if there are no other basis to define it. And it's back to pure Hilbert space vectors with unit trace 1.

So the question is.. what kind of information can be stored in the Hilbert space nonorthogonal states? How complex the information it can hold? Can they store a Barbie doll information? or nothing? just want to have idea...

 

[PeterDonis]

suppose that this trajectory can be explained theoretically by two different Hamiltonians

Is this possible? Can you give an actual example?

 

[atyy]

Consider a physical system in which the average value of position is $<x>=0$. What is the probability that the position is $x=1$ nm?

To be more conventional, one can use the term "expectation" in place of "average". Conceptually, there is no difference. You can see A. Neumaier's post #78 for the mathematical fine print.

 

[Demystifier]

Ok, mathematically.. if we remove the position basis.. then there would be no decoherence and no subsystems if there are no other basis to define it. And it's back to pure Hilbert space vectors with unit trace 1.

Yes.

 

[Demystifier]

Is this possible?

Yes.

Can you give an actual example?

Solution $x(t)=0$.
$$H_1=\frac{p^2}{2m}$$
$$H_2=\frac{p^2}{2m}+\frac{k x^2}{2}$$