Functional information

The concept of functional information is an attempt to rigorously define the information content of biological systems. The concept was originated by a group led by Jack W. Szostak in 2003.

Definition

They define functional information as follows:

• the concept of degree of function is introduced, where the degree of function $E_{x}$ is a non-negative objective measure of the capability of system $E$ to do the physical function $x$.
• the fraction of possible configurations of the system that can achieve at least a particular level of function $\theta$ in regard to tthe physical function $x$ is defined to be $F(E_{x}\geq \theta )$
• the functional information relstive to a given level of function $E_{x}=\theta$ is defined as $I(E_{x}\geq \theta )=-log_{2}F(E_{x}\geq \theta )$

This leads to two conclusions:

• because all possible configurations can achieve zero or more functionality, that is to say $F(E_{x}\geq 0)=1$, the minimum possible functional information for a system is $-log_{2}1$, which is zero.
• for the highest possible level of a degree of function of a system $E_{x}=\theta _{max}$, there will be a well defined $I(E_{x}=\theta _{max})=-log_{2}F(E_{x}=\theta _{max})$

Note that functional information of a system $E$ must always be defined relative to a specific function $x$, without a choice of which it has no meaning.

Law of increasing functional information

In 2025, a group of researchers proposed a law of increasing functional information, that asserts that a tendency to increase in functional information is an inherent property of the universe, encompassing both biological and non-biological systems.

See also

• Entropy and life
• Second law of thermodynamics
• Specified complexity, a creationist pseudoscientific concept