Polarization-division multiplexing (PDM) has emerged as a promising technique for increasing data rates without increasing symbol rates. However, the distortion effects of the fiber transmission medium poses severe barriers for the implementation of this technological alternative. Especially, due to the fiber-induced polarization fluctuation orthogonally transmitted PDM signals are mixed at the receiver input. Therefore, a receiver compensation structure needs to be implemented to recover the original orthogonal transmitted components from their mixtures at the end of the fiber channel. This is in fact the focus of this article where a receiver algorithm is based on a recently proposed minimum entropy equalization scheme exploiting the maximization of (an enhanced) energy cost function subject to the magnitude boundedness of (incoming) digital communication signals. Through the use of this scheme, new receiver algorithms for recovering the original polarization signals in an adaptive manner are proposed. The key feature of these algorithms is that they can achieve high equalization performance while maintaining the algorithmic complexity in a fairly low level that is suitable for implementation in optical fiber communication receivers. The performance of these algorithms for a square-QAM based coherent polarization division multiplexed system are illustrated through some simulation examples.