minimum value from uniform_real_distribution()

In my program, I generate uniform random numbers between 0 and 1 using uniform_real_distribution()

#include <random>

default_random_engine e;
uniform_real_distribution<double> u(0,1);

double rand_num = u(e);

I'm wondering that what is the minimum value of the generated random number except 0. i.e. minimum gap between two random number.