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.^[1]

They define functional information as follows:^{[2] [3]}

• the concept of degree of function is introduced, where the degree of function ${\displaystyle E_{x}}${\displaystyle E_{x}} is a non-negative objective measure of the capability of system ${\displaystyle E}${\displaystyle E} to do the physical function ${\displaystyle x}${\displaystyle x}.
• the fraction of possible configurations of the system that can achieve at least a particular level of function ${\displaystyle \theta }${\displaystyle \theta } in regard to the physical function ${\displaystyle x}${\displaystyle x} is defined to be ${\displaystyle F(E_{x}\geq \theta )}${\displaystyle F(E_{x}\geq \theta )}
• the functional information relative to a given level of function ${\displaystyle E_{x}=\theta }${\displaystyle E_{x}=\theta } is defined as ${\displaystyle I(E_{x}\geq \theta )=-log_{2}F(E_{x}\geq \theta )}${\displaystyle 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 ${\displaystyle F(E_{x}\geq 0)=1}${\displaystyle F(E_{x}\geq 0)=1}, the minimum possible functional information for a system is ${\displaystyle -log_{2}1}${\displaystyle -log_{2}1}, which is zero.
• for the highest possible level of a degree of function of a system ${\displaystyle E_{x}=\theta _{max}}${\displaystyle E_{x}=\theta _{max}}, there will be a well defined ${\displaystyle I(E_{x}=\theta _{max})=-log_{2}F(E_{x}=\theta _{max})}${\displaystyle I(E_{x}=\theta _{max})=-log_{2}F(E_{x}=\theta _{max})}

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

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.^{[4] [5] [6]}

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

• Information theory
• Measures of complexity
• Biology
• Biophysics
• Biophysics stubs

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