Syneresis exhibited by a heterogeneous polyampholyte coacervate (polymer-rich phase) is discussed through non-equilibrium statistical thermodynamics. It has been shown that the coacervate phase is associated with fluctuating excess internal pressure that gives rise to syneresis. It is proposed that energy is dissipated to the environment only by the surface of coacervate, whereas in the bulk, gelatin chains only exchange energy with each other with negligible or no dissipation. Consequently, the internal pressure inside the coacervate follows a damped oscillatory behaviour that relaxes slowly with time, independently of amplitude. We connect the volume of the supernatant released with time (exponential relaxation behavior) with the presence of long-lived nonlinear localized modes (the existence of breathers).