Joint Entropy

The entropy associated with events like 'a particle is leaving compartment i and entering compartment j' is usually called the joint entropy Hoi

Also, we can define probabilities associated with events 'a particle enters compartment j' (from any other compartment) as well as 'a particle leaves compartment i' (to any other compartment):

Table 2 Contribution of every coefficient to the joint entropy

Hl,O

Table 2 Contribution of every coefficient to the joint entropy

Hl,O

Imp.

A

B

C

D

Exp.

Diss.

Imp.

0

0.52

0

0

0

0

0

A

0

0

0.41

0.31

0

0

0.25

B

0

0

0

0.09

0.28

0.15

0.15

C

0

0

0

0

0.25

0

0.2

D

0

0

0

0

0

0.25

0.28

Exp.

0

0

0

0

0

0

0

Diss.

0

0

0

0

0

0

0

Table 3

Contribution of every compartment to the input

entropy H

Imp.

A

B

C

D

Exp.

Diss.

0

0.52

0.41

0.34

0.39

0.31

0.47

calculation takes the form — (tj/t )log(tf/t.) . The resulting entropy will be HI = 2.459. Using row sums in a similar manner, we can see that the entropy associated with outputs is HO = 2 .192.

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