# Entropy, Fluctuation Magnified and Internal Interactions

## Abstract

**:**

_{r}(t) ln P

_{r}(t). From this or S = k ln Ω in an internal condensed process, possible decrease of entropy is calculated. Internal interactions, which bring about inapplicability of the statistical independence, cause possibly decreases of entropy in an isolated system. This possibility is researched for attractive process, internal energy, system entropy and nonlinear interactions, etc. An isolated system may form a self-organized structure probably.

## INTRODUCTION

## FLUCTUATION MAGNIFIED AND UNEQUAL PROBABILITY

_{r}> 0 . For these cases of the increasing probability dP

_{r}> 0, and 1 > 1 + ln P

_{r}> 0, so

_{r}= −k (1 + ln P

_{r})dP

_{r}< 0.

_{r}decreases when the probability of a state r increases. It is consistent with the disorder decrease when the determinability increases. In this case, S

_{r}is additive.

_{fm}= 1/ n > P

_{r}.

n= | 10 | 5 | 3 | 2 |

dS/k= | -0.0843 | -0.2982 | -0.6810 | -1.2729 |

_{f}= 0, dS = −dS

_{i}=-3.9120k. So the entropy decreases necessarily.

## ATTRACTIVE PROCESS

_{1}= n!. Assume that internal attractive interaction exists in the system, the n-particles will cluster to m-particles. If they are in different states of energy still, then Ω

_{2}= m!. Therefore, in this process

_{2}− S

_{1}= dS = k ln(Ω

_{2}/ Ω

_{1}) = k ln(m!/ n!) .

_{r}= 1/n, S

_{1}= k ln n . These particles cluster to the equal-probable m-particles, S

_{2}= k ln m, dS = k ln(m / n) . The conclusion is the same. We have discussed the possibility on decrease of entropy, its mechanism and some examples [6]. Here from the definition of entropy a possibly developed direction is researched.

_{s}is the additive part of the particle energy in the state s, in most cases it and E are the kinetic energy; W

_{ss'}and U

_{ss'}are the absolute values of the attraction and repulsion energies of particles in the states s and s’, respectively.

^{a}+ dS

^{i},

^{a}is an additive part of entropy, and dS

^{i}is an interacting part of entropy. Eq.(19) is similar to a well known formula:

_{i}S + d

_{e}S,

^{2}may be gravitational or electromagnetic force. The potential energy is

## SYSTEM ENTROPY AND NONLINEARIRY

_{1}) + S(ρ

_{2}) ,

_{1}ρ

_{1}+ λ

_{2}ρ

_{2}[13]. This shows that the entropy decreases with the internal interaction. Not only is this conclusion the same with the conditioned entropy on ρ

_{1}and ρ

_{2}, but also it is consistent with the systems theory in which the total may not equal the sum of parts.

_{2}> S

_{1}When (∂V

_{2}/ ∂T

_{2}) < (∂V

_{1}/ ∂T

_{1}); conversely, S

_{2}< S

_{1}when (∂V

_{2}/ ∂T

_{2}) > (∂V

_{1}/ ∂T

_{1}).

_{i}= S

_{0}+ c

_{V}ln T + vR ln V .

_{2}> θ

_{1}for the attraction cases, then S

_{2}< S

_{2}, and the entropy will decrease.

## DISCUSSION

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**MDPI and ACS Style**

Chang, Y.-F.
Entropy, Fluctuation Magnified and Internal Interactions. *Entropy* **2005**, *7*, 190-198.
https://doi.org/10.3390/e7030190

**AMA Style**

Chang Y-F.
Entropy, Fluctuation Magnified and Internal Interactions. *Entropy*. 2005; 7(3):190-198.
https://doi.org/10.3390/e7030190

**Chicago/Turabian Style**

Chang, Yi-Fang.
2005. "Entropy, Fluctuation Magnified and Internal Interactions" *Entropy* 7, no. 3: 190-198.
https://doi.org/10.3390/e7030190