In order to have two independent noise sources with a different random seed the rand(), or random(), or white() LTSpice-functions have to be called with a different argument, e.g.:
Note however, the pseudo random numbers output of the function white is NOT Gaussian white noise as the name might suggest, see also this post: https://www.linkedin.com/pulse/ltspice-rand-white-jean-francois-debroux/
Generate Gaussian white noise (GWN) distributed pseudo random numbers from independent identically distributed (IID) random numbers using the Box-Muller transform:
with mean and standard deviation . Note, that the two iid pseudo random numbers generated using the LTSpice rand()-function have to have different seed.
As soon as I find the time I will check how well that works in LTSpice and provide plots and statistics. Any feedback is very welcome.