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International review of physics

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

Yi‐Fang Chang

Published Aug 31, 2013• 6 citations
Publisher

Abstract

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.

DOI
10.15866/irephy.v7i4.4440

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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.
We propose that a necessary condition of decrease of entropy in isolated system is existence of internal interactions. Then a theoretical development and some possible examples on decrease of entropy are researched. In quantum region, in particular for some Bose systems, decrease of entropy is more possible. The base of violation of Pauli exclusion principle is unified quantum statistics and attractive interactions, which corresponds also to decrease of entropy with internal interactions. Perhaps, some basis principles have essential relations.
The present experimental tests have proved high precisely the validity of the Pauli exclusion principle (PEP) in usual cases. The future experiments should be combined widely with various theories of hidden and obvious violation of PEP. Author think that known experiments and theories seem to imply the violation at high energy. Some possible tests have been proposed in particle physics, nuclei at high energy and astrophysics, etc., in particular, the excited high-n atoms and multi-quark states. Moreover, the violation is possibly relevant to the nonlinear quantum theory, in which the present linear superposition principle may not hold. Finally, the possible violation at very low temperature is discussed. These experiments may be connected with tests of other basic principles, for example, the present wave property, possible decrease of entropy due to internal interactions in isolated systems, and PCT invariance, etc.
First, we point out that the present applied superposition principle is linear, it must be developed into a generality. Next, the linear operators and equations should be developed nonlinearly. They will include nonlinear Klein-Gordon equation and Dirac equations, and corresponding Heisenberg equation. The quantum commutation and anticommutation should be developed. This theory may include the renormalization, which is the correction of Feynman rules of curved closed loops. We think the interaction equations are nonlinear. Many theories, models and phenomena are all nonlinear, for instance, soliton, nonabelian gauge field, and the bag model, etc. The superluminal entangled state, which relates the nonlocal quantum teleportation and nonlinearity, should be a new fifth interaction. Moreover, the NL effects exist possibly for four interactions, for single particle, for high energy, and for small space-time, etc. The relations among NL theory and electroweak unified theory, and QCD, and CP nonconservation, etc., are expounded. Finally, some known and possible tests are discussed. The NL theory relates the possible decrease of entropy in isolated system.