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Updated: Dec 11, 2025

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
Published on: April 8, 2020
Entropy formula of N-body system
1Materials and Life Science Research Division, Korea Institute of Science and Technology, and Major of Nanomaterials Science and Engineering, KIST Campus, Korea University of Science and Technology, 5 Hwarang-ro 14-gil, Seongbuk, Seoul, 02792, Republic of Korea. jae-wan.shim@kist.re.kr.
Abstract:
We prove a proposition that the entropy of the system composed of finite N molecules of ideal gas is the q-entropy or Havrda-Charvát-Tsallis entropy, which is also known as Tsallis entropy, with the entropic index [Formula: see text] in D-dimensional space. The indispensable infinity assumption used by Boltzmann and others in their derivation of entropy formulae is not involved in our derivation, therefore our derived formula is exact. The analogy of the N-body system brings us to obtain the entropic index of a combined system [Formula: see text] formed from subsystems having different entropic indexes [Formula: see text] and [Formula: see text] as [Formula: see text]. It is possible to use the number N for the physical measure of deviation from Boltzmann entropy.
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