Abstract
AbstractWe 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 $$q=\frac{D(N-1)-4}{D(N-1)-2}$$
q
=
D
(
N
-
1
)
-
4
D
(
N
-
1
)
-
2
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 $$q_C$$
q
C
formed from subsystems having different entropic indexes $$q_A$$
q
A
and $$q_B$$
q
B
as $$\frac{1}{1-q_C}=\frac{1}{1-q_A}+\frac{1}{1-q_B}+\frac{D+2}{2}$$
1
1
-
q
C
=
1
1
-
q
A
+
1
1
-
q
B
+
D
+
2
2
. It is possible to use the number N for the physical measure of deviation from Boltzmann entropy.
Funder
Korea Institute of Science and Technology
Publisher
Springer Science and Business Media LLC
Reference23 articles.
1. Havrda, J. & Charvát, F. Quantification method of classification processes. Concept of structural a-entropy. Kybernetika 3, 30–35 (1967).
2. Tsallis, C. Possible generalization of Boltzmann–Gibbs statistics. J. Stat. Phys. 52, 479–487 (1988).
3. Tsallis, C. Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World (Springer, New York, 2009).
4. Cho, A. A fresh take on disorder, or disorderly science?. Science 297, 1268–1269 (2002).
5. Plastino, A. R. & Plastino, A. Stellar polytropes and tsallis’ entropy. Phys. Lett. A 174, 384–386 (1993).
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