Statistical Distribution of a Completely Open System Based on Incomplete Shannon Entropy

Micro canonical, canonical and grand canonical systems are special cases of completely open systems. Within the framework of non-extensive and incomplete statistics, we derive the statistical distribution for a completely open system on the basis of incomplete Shannon entropy, using the maximum entropy principle. We calculate the physical properties of a linear filament using this distribution. The results are the same as those calculated using the incomplete E-V distribution, except that average values of the thermodynamic variables replace the corresponding constant values. However, the relative fluctuations in thermodynamic variables are completely different. In the canonical and grand canonical distributions, relative fluctuations are proportional to l/√N. In the incomplete statistical distribution for a completely open system, the relative fluctuations are proportional to 1. This result can explain some phenomenon that traditional and current statistical mechanics cannot explain, such as the large fluctuations of critical, super-cooled and overheated states.