  We develop an accurate, highly efficient and scalable random batch Ewald
(RBE) method to conduct simulations in the isothermal-isobaric ensemble (the
NPT ensemble) for charged particles in a periodic box. After discretizing the
Langevin equations of motion derived using suitable Lagrangians, the RBE method
builds the mini-batch strategy into the Fourier space in the Ewald summation
for the pressure and forces so the computational cost is reduced from
$\mathcal{O}(N^2)$ to $\mathcal{O}(N)$ per time step. We implement the method
in the LAMMPS package and report accurate simulation results for both dynamical
quantities and statistics for equilibrium for typical systems including
all-atom bulk water and a semi-isotropic membrane system. Numerical simulations
on massive supercomputing cluster are also performed to show promising CPU
efficiency of RBE.
