Biology - Molecular Theory of the Living Cell - page 98

Table 4.3 (continued)
g The subsethood is defined here as follows. When (1) all the elements of set A are also the
elements of set B but (2) not all the elements of B are the elements of A, set A is referred to as the
subset of B which is denoted as A I

h Thermodynamics is the study of the energy and thermodynamic entropy changes accompanying
physicochemical processes of material systems, whereas informatics is the study of the informa-
tional changes accompanying both physicochemical processes and their consequents, namely,
mental processes and their causations
i According to the Information-Energy Complementarity Principle (Sect. 2.3.2 ) , thermodynamics
and informatics are complementary disciplines both of which are essential for a complete
understanding/description of nature, including the phenomenon of life

< B. In this sense, S is a subset of I, i.e. ,S <

consideration. If this principle applies here, both Ben-Naim's and my suggestions to
the solution of the entropy-information debates may be considered complementary ,
the former prescinding (Sect. 6.2.12 ) the informational aspect and the latter taking
into account both the energy and entropy (i.e., free energy) aspects, in agreement
with the information-energy complementarity thesis (see Row 10 in Table 4.3 )
(see Sect. 2.3.2 ).

4.8 The Minimum Energy Requirement for Information
Transmission

In addition to Eq. 4.2 that defines what was later referred to as the Shannon entropy,
H, Shannon derived another important equation, the channel capacity equation ,
Eq. 4.29 :

C ¼ W log 2 ð 1 þ P = N Þ bits = s (4.29)

where C is the channel capacity or the capacity for a communication channel to
transmit information in unit time, W is the bandwidth of the channel or the range of
frequencies (also called the “degree of freedom”) used in communication, P is the
power or the rate of energy dissipation needed to transmit the signal, and N is the
thermal noise of the channel.
According to Eq. 4.29 , when no power is dissipated, i.e., when P 0, the

channel capacity C is zero, indicating that no information can be transmitted
through the channel. Calculations show that the amount of energy needed to
transmit the minimum amount of information, i.e., 1 bit, is 0.6 kcal/mol or 2.4
Joules/mol (Pierce 1980). Therefore, it is possible to formulate the following
general statement which may be referred to as the Principle of Minimum Energy
Dissipation for Information Transmission (PMEDIT):
It is impossible to transmit information without dissipating energy.

¼

(4.30)