The Tsallis statistical distribution in a completely open system

Incomplete <i>E-V</i> Distribution for Shannon Entropy

“…The current statistical physics (extensive statistics that is also called BGS; nonextensive statistics and incomplete statistics) usually take micro canonical systems, canonical systems and grand canonical systems as the research objects (We derived the statistical distribution for a completely open system [11] within the framework of Tsallis statistics recently, taking the completely open systems as the research objects). Micro canonical systems are completely isolated, they neither exchange heat nor work with environment, their corresponding distributions are called 0 distributions; canonical systems have variable energy E, constant volume V and constant particle number N, they exchange heat but not work with environment, so canonical distributions are called E distributions; grand canonical systems have variable energy E, variable particle number N and constant volume V, they exchange heat and particle number but not work with environment, so grand canonical distributions are called N-E distributions; E-V systems (have constant particle…”

“…In the theory of "dissipative structure," a new ordered structure is produced from fluctuations [10]. It is therefore necessary to discuss the E-V and N-E-V distributions [11] with alterable extent. In this paper, the E-V distribution is derived based on deformed Shannon entropy (Shannon entropy would be nonextensive if interactions were considered) within the framework of incomplete statistics, and revisions of traditional statistical mechanics with different values of parameter q are discussed, taking a linear filament as an example (with changing extent, some biomacromolecules such as DNA have the structure of a linear filament).…”

Incomplete statistics in a completely open system based on incomplete entropy

“…We introduced microscopic volume which was suggested in reference [23] into incomplete statistics, and obtained a constraint related to volume:…”

“…The phase rule of extensive statistical mechanics therefore does not hold. Introducing a microscopic volume, we derived the statistical distribution for a completely open system based on Tsallis entropy [23]. Our results are not limited to small systems.…”

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

“…We deduced the statistical distribution of a completely open system and a few thermodynamic formulas by applying Tsallis entropy [1] and the maximum entropy principle in our previous paper [2]. However, even with these tools it is still complicated to study the thermodynamic properties of a completely open system with the Tsallis statistical distribution.…”