  Non-reciprocal interactions between scalar fields that represent the
concentrations of two active species are known to break the parity and
time-reversal (PT) symmetries of the equilibrium state, as manifested in the
emergence of travelling waves. We explore the notion of nonlinear
non-reciprocity and consider a model in which the non-reciprocal interactions
can depend on the local values of the scalar fields. For generic cases where
such couplings exist, we observe the emergence of spatiotemporal chaos in the
steady-state. We associate this chaotic behaviour with a local restoration of
PT symmetry in fluctuating spatial domains, which leads to the coexistence of
oscillating densities and phase-separated droplets that are spontaneously
created and annihilated. We uncover that this phenomenon, which we denote as
effervescence, can exist as a dynamical steady-state in large parts of the
parameter space in two different incarnations, as characterized by the presence
or absence of an accompanying travelling wave.
