# Negative entropy

In thermodynamics, negative entropy (TR:164) (LH:1) (TL:165), as compared to “positive entropy” (TR:9), refers to the invented quantity , i.e. the negative value of entropy, introduced in 1943 by Erwin Schrodinger, an semi-floundered attempt to conceptualize a laymanized model for "order", thermodynamically speaking.

## Overview

In 1943, Erwin Schrodinger, in his What is Life? lecture-turned-book, in his attempt to explain when matter is "alive", in the context of the second law, citing Boltzmann and Gibbs, gave the following formula for what he called the statistical meaning of entropy:

${\displaystyle S=k\log D}$

where S is entropy, k is the Boltzmann constant and D is a "quantitative measure of the atomistic disorder of the body in question," as he says. Correctly, D, used here, refers to Boltzmann's W or multiplicity, which tends to refer to the probability distribution of a body, not specifically a measure of "atomistic disorder", as Schrodinger sees things.[1] In any event, Schrodinger then declares:

“The second law is a fundamental law of physics which refers to the natural tendency of things to approach the chaotic state.”
— Erwin Schrodinger (1943), What is Life (pg. 73)[2]

To clarify, in the "standard model of entropy", originated by Clausius (1865), employed by Gibbs (1872, 1901), and later Lewis (1923), the term "disorder" is not used one time! The association of "disorder" of bodies and entropy, was a latter addition to theory, added on in part by Ludwig Boltzmann (1890s), but predominately by Max Planck (1900s), and is not a universally applicable model. Whatever the case, in the early 20th century, the disorder model of entropy began to proliferate, for some reason?

Hence, Schrodinger says that if D is a "measure of disorder", than its reciprocal, as shown below, can be regarded as a "direct measure of order":

${\displaystyle {\text{Order}}={\frac {1}{D}}}$

or:

${\displaystyle {\text{Order}}=D^{-1}}$

If we substitute D-1, aka "order" according to Schrodinger, into the right side of Schrodinger's version of the entropy formula, so to obtain some type of function that is a quantitative measure of atomistic order, we get:

${\displaystyle F({\text{order}})=k\log D^{-1}}$

Hence, according to the following rule for logarithms:

${\displaystyle \log(a^{b})=b\log(a)\,\!}$

we find that Schrodinger's order function is the following:

${\displaystyle F({\text{order}})=-S}$

or the negative value of entropy, which Schrodinger calls "negative entropy", as though it were some type of new thermodynamic function?

### Negentropy

In 1950, Leon Brillouin, in his “Thermodynamics and Information Theory”, abbreviated "negative entropy"[3] term to the new term "negentropy"[4], which only added to the confusion.

### Discussion

In 1975, Norman Dolloff, in his Heat Death and the Phoenix, was the first to state that Schrodinger's order and disorder model of entropy, was not fully correct; whereas, correctly, it is the Gibbs energy that defines the formation energy of a thing, and hence its relative order or disorder, not solely entropy alone.

## Negative free energy?

In 2000s, Jurgen Mimkes, in his socio-economic thermodynamics publications, similar in theme to Schrodinger's confusing use of putting "negative" sign in front of a thermodynamics variable and calling it a new function, began to put a negative sign in front of Gibbs energy G and also in front of differentials of Gibbs energy dG; some examples of which are as follows:

“The state of large stochastic systems of N objects may be calculated by the Lagrange principle L(N) = T log P(N) + E(N) → maximum ! P is the probability, that is to be maximized under a system condition E, and T is the Lagrange ordering parameter. L is the Lagrange function of the system, that may be far away or close to stability. At equilibrium the Lagrange function is at maximum. In natural sciences E is given by the chemical bonds and the (negative) Lagrange function corresponds to the free energy, from which all thermodynamic states may be calculated. In social systems the Lagrange principle corresponds to the common benefit. The function E represents the social bonds of the system.”
— Jurgen Mimkes (2002), “The Structure of Complex Systems: Thermodynamics, Socio-Economics”
“The system – solid or social – will be stable only if the negative free energy (-dG) is at a maximum. This idea goes back to Empedocles (450BC), who in his On Nature explains that solubility of wine in water similar to love of relatives, and Goethe (1809) who in his Elective Affinities demonstrated that love and marriage depend on the physico-chemical laws of society.”
— Jurgen Mimkes (2012), Chemistry of the Social Bond (Ѻ)
“People are not spins. People are elements or agents with ‘attractions’ or ‘dis-attractions’. So what people can do is they can attract each other, if the [free] energy is positive [-dG > 0] or they can dis-attract (repel) each other if the [free] energy is negative [-dG < 0], and they can be indifferent if the interaction energy is zero [dG ≈ 0].
— Jurgen Mimkes (2016), “On Goethe’s affinities vs modern free energies”; Interview by Libb Thims at the BPE 2016 conference, Washington DC

This reason for confusing use of this negative sign did not become known until Libb Thims, during his interview of Mimkes, asked him about this, and he said that he added it into so that it would be easier to say that when free energy is maximized, in a relationship or social system, that to is love or social well-being maximized, accordingly.

This, however, only makes for confusion, e.g. when one looks at the situation graphically, e.g. on a reaction coordinate, or when one has to speak about how "negative free energy change", i.e. ΔG < 0 or dG < 0, is the criterion for spontaneity in a chemical reaction. Hence, a statement such as "negative free energy (-dG) is at a maximum", only makes for confusion, just as is the case with Schrodinger's "negative entropy".

## Quotes

The following are related quotes:

“My remarks on negative entropy have met with doubt and opposition from physicist colleagues.”
— Erwin Schrodinger (1943), What is Life (pg. #)[2]

## End matter

### References

1. Multiplicity – Hmolpedia.
2. Schrodinger, Erwin. (1943). What is Life? The Physicist's approach to the Subject: with an Epilogue on Determinism and Free Will (§: Note to Chapter 6). Cambridge, 1944; 2012.
3. Negative entropy – Hmolpedia 2020.
4. Negentropy – Hmolpedia 2020.