You can characterize the noise using things like temperature and material properties. But you cannot simulate the system, you cannot reproduce it, the noise its

You can characterize the noise using things like temperature and material properties. But you cannot simulate the system, you cannot reproduce it, the noise itself is the result of subatomic particles interacting. Two resistors made of the exactly same material, the same cristaline structure down to every atom and heated in the same way up from 0K will generate different noise.