Law of information

The First Law in Information Theory

1. Law of Conservation of Information: or law of conservation of total states.

It sum of states that the total (created) inflow of useful or significative or existent information into a system with the total (destroyed) outflow of trashy or nonsensical (meaningless, insignificant) or disappeared (vanish, dissolve) information from the system must equal total information, original and destroyed (plus) the change in the information contained within the system. In other words, information can be converted from one form to another, all appearance it can be created or destroyed, but total information or states or entropy is to equal sum of sub-states, sub-information, sub-entropy, total information is conservation, together increase or together decrease, or one increase with one decrease.

Equation

∑ni=N

or

Ω=∑ωi（2）

Ωi=∑ωij

Ω=∑Ωi=∑∑ωij

entropy conservation:

klgΩ=∑klgωi

Si=klgωi

S=∑Si （3）

signal (information) conservation:

I=∑Ii=-∑PilgPi

I=∑Iuse+∑Ino

N=∑nusei+∑nnoi

(DENG Yu, et al, Journal of Math. Medicine (Chinese),2000, 13: 88–89)

(http://www.oridream.com/) There come from ∑Pi=1.

S=∑(Sincr+Sdec)

Conservation of Entropy is increase entropy + decrease entropy must equal total Entropy.

or

I=∑(Iinc+Idec)

Conservation of Information is increase Information + decrease Information must equal total Information.