  Bubble-nucleation processes of a Lennard-Jones liquid are studied by
molecular dynamics simulations. Waiting time, which is the lifetime of a
superheated liquid, is determined for several system sizes, and the apparent
finite-size effect of the nucleation rate is observed. From the cumulative
distribution function of the nucleation events, the bubble-nucleation process
is found to be not a simple Poisson process but a Poisson process with an
additional relaxation time. The parameters of the exponential distribution
associated with the process are determined by taking the relaxation time into
account, and the apparent finite-size effect is removed. These results imply
that the use of the arithmetic mean of the waiting time until a bubble grows to
the critical size leads to an incorrect estimation of the nucleation rate.
