Mathematics

The idea of the verbal expression 'negative entropy' being synonymous to 'order' stems from a combination of the following three expressions:

Rule for inverse functions Rule for logarithms Entropy expression from statistical mechanics.

In short, Schrodinger equates the multiplicity W of the Boltzmann entropy equation with disorder, pure and simple, which he reasons applied to all systems; then equates the inverse of multiplicity with order, as in:

then carries the negative sign over to the left side of the statistical entropy expression, using the rule for logarithms, to argue that negative S equals order.

Derivation

In his 1944 book

where

or

Hence, as Schrödinger states:

“The awkward expressionnegative entropycan be replaced by a better one: entropy, taken with the negative sign [ – entropy], is itself a measure of order.”

Thus, he concludes “the device by which an organism maintains itself stationary at a fairly high level of orderliness”, a state he equates with a low level of entropy, consists in “sucking orderliness from its environment”.

Negentropy

In 1953, through the guise of information theory, Schrödinger's

Difficulties

After his lecture, wherein he discussed negative entropy, Schrodinger famously had to add a note to Chapter 6, where explains that:

“My remarks onnegative entropyhave met with doubt and opposition from physicist colleagues.”

He goes on to explain that had he been lecturing to them, he would have turned the discussion to free energy, but judged the concept too intricate for the lay audience. In a 1946 review of Schrödinger’s

See also

● Positive entropy

References

1. Schrödinger, Erwin. (1944).

2. Brillouin, Léon. (1953). "Negentropy Principle of Information",

3. Muller, H. J. (1946). “A physicist stands amazed at genetics.” (PDF).

4. Stockard U. von and Liu, J. S. (1999). “Does Microbial Life Always feed on Negative Entropy? Thermodynamic Analysis of Microbial Growth.”

Further reading

● Iniquez, Cruz. (2008).