Microsystems for Bioelectronics

Clearly from (A3), each of the probabilities is equal to the same constant and we must have that the

sum of the probabilities is one, i.e.,

X

K

i ¼1

p

i

¼ 1 ¼ Ke

l

C

1

(A4)

(A4) can be solved for

l

to yield

l ¼ C



1 þ ln



1

K



(A5)

The substitution of (A5) into (A3) yields the choice for probabilities that maximize (A1):

p



i

¼ e



C½1 þ lnð1 = KÞ

C

 1



¼ e

ln



1

K



¼

1

K

; i ¼ 1; 2; . ; K (A6)

The maximum value of the information entropy that results is

 C

X

K

i ¼1

p



i

lnðp



i

Þ¼C

X

K

i ¼1

1

K

ln



1

K



¼ C lnðKÞ (A7)

LIST OF SYMBOLS

Symbol Meaning

A Area

b Computational base, logarithm base

C Constant

E Energy

f Frequency

F Bit rate

I Information

k

B

Boltzmann constant, k

B

¼ 1.38  10

–23

J/K

K, L, N Integer numbers

l Length

m Mass

M Molar mass

N

A

Avogadro’s Number, N

A

¼ 6.022  10

23

mol

–1

p Probability

P Power

Q Heat flux

r, R Radius

S Entropy

182 CHAPTER 6 Micron-sized systems: In carbo vs. in silico