This is a both physics and math question.
I have a Hamiltonian in the form
H= q1^2 + q2^2 + q3^2 + q1 x q2 x q3
Therefore the probability distribution will have the form
p= exp ^ (-bH)
where b is beta/k_b*T
Now, I want to know if this probability function is separable, that is if I can write it as
p= exp ^(-b*f(q1)*f(q2)*f(q3))
where f functions are single variable functions of their arguments. I will need to check this condition for many other Hamiltonians so I want to know if there is a generally applicable test to check whether they are separable.
Cheers