Unified Quantum Statistics, Possible Violation of Pauli Exclusion Principle, Nonlinear Equations and Some Basic Problems of Entropy

We propose that Bose-Einstein (BE) and Fermi-Dirac (FD) distributions may be unified by the nonlinear quantum equation. Further, the unified quantum statistics and possible violation of Pauli exclusion principle (PEP) at high energy are researched. Third, we propose a possibility of entropy decrease due to internal interactions in some isolated systems, in particular, for quantum statistics. Fourth, we discuss a new type of soliton equation, whose solutions may describe some statistical distributions. Finally, the moderate input negative entropy flow for open systems, etc., are investigated.