11:29 PM
@Feynman_00 Here's something that will bake your noodle:
In a classical description of a particle in contact with a heat bath, you can add a "noise" term to the particle's motion. For example: $m \ddot{x}(t) = - \gamma \dot{x}(t) + \eta(t)$.
That's the so-called Lengevin equation. It's just Newton's F=ma where the force has a friction term $-\gamma \dot{x}$ and a "noise" term $\eta(t)$.
The function $\eta$ is basically random at each point in time.
There are some interesting ways in which $\gamma$ and $\eta$ have to be related, otherwise the system has unphysical properties.
However, in a quantum description, the relationship between the friction and the noise comes automatically. Basically, because everything in quantum is unitary, you can't just make up a friction or noise term... you have to actually add extra quantum degrees of freedom, and those degrees of freedom give you the friction and the noise together.