The combined effects of finite ionic sizes and boundary slip on the entropy generation in mixed pressure driven and electroosmotic flows (EOFs) in a soft nanochannel are investigated in this study. The soft nanochannel is represented by a rigid nanochannel covered by a charged polyelectrolyte layer (PEL) on its surface. The entropy generation analysis of EOFs in such a soft nanochannel is addressed for the first time. Under the assumption of high zeta potentials, the electric potential, velocity, and temperature distributions are obtained numerically by using the finite difference method. Subsequently, the thermal transport characteristic and the corresponding entropy generation analysis are discussed based on the obtained velocity and temperature distributions. Our results show that the soft nanochannel in the present model is not appropriate for cooling purposes. We also demonstrate that the steric factor v and the PEL thickness d can enhance the entropy generation rate. However, the slip boundary coefficient γ, the drag parameter α, and the equivalent electric double-layer (EDL) thickness λFCL can restrain this entropy generation rate. In addition, the contributions of Joule heating and viscous friction in the entropy generation rate are more prominent than the contribution due to heat transfer. The present theoretical research can be used to design the efficient thermofluidic devices.