  We present a phase space study of non-Hermitian Hamiltonian with
$\mathcal{PT}$-symmetry based on the Wigner distribution function. For an
arbitrary complex potential, we derive a generalized continuity equation for
the Wigner function flow and calculate the related circulation values. Studying
vicinity of an exceptional point, we show that a $\mathcal{PT}$-symmetric phase
transition from an unbroken $\mathcal{PT}$-symmetry phase to a broken one is a
second-order phase transition.
