Zenodo .org is good web site run by CERN to post non peer reviewed preprints

[Rama Iyer]

I placed it on Zenodo . It’s downloaded 1:33 GB . Does anybody know how E Schrodinger got the expression W/KT = 30 to 60 which when fitted into the mentioned Polyani -Wigner expression gives time of expectation of mutation of virus to 3000 years as given by  Schrodinger in the book What is life? . The question is how did he get W/KT = 30 to 60 . The book you can download using Firefox server. Just type What is life ? By E Schrodinger. 

Source: Zenodo The search for relevance in Erwin Schrodinger's mutations and mathematical interlude from his book " What is Life?" to COVID-19 mutations and variants https://share.google/ygh8FZcljgqK4jWhm

 

Kind regards 

Rama 

[Paola Di Maio]

Rama, to your question 

it is not my field but... unless some experts want to correct it//

CHATGPT says//

Great question — and it looks mysterious if you only see the final numbers.
But the key is: Schrödinger did not calculate the value W/kT = 30–60.
He assumed it based on known activation energies of chemical bond rearrangements available in 1930s physical chemistry.

Let’s break it down clearly.

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1. What is W/kT?

• W = activation energy needed to break or change a chemical bond (in mutation terms: a bond change in a gene).

• kT = thermal energy per degree of freedom at body temperature (~300 K).

So W/kT is the energy barrier measured in units of thermal fluctuations.

If W/kT≫1, thermal fluctuations almost never trigger the event spontaneously.

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2. Schrödinger Used Known Chemistry Values

In the 1930s–40s, chemists like Eyring, Wigner, and Polanyi had measured typical bond activation energies:

W≈0.6 to 1.2 eV

At physiological temperature:

kT≈0.026 eV

So:

kTW≈0.0260.6−1.2≈23−46

Rounded to account for biological complexity:

kTW≈30−60

So the ratio comes directly from typical chemical bond strengths.

No exotic derivation — just plugging in known physical chemistry constants.

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3. How This Enters the Polanyi–Wigner Relation

The Polanyi–Wigner equation for spontaneous activation events is:

rate∼νe−W/kT

where ν is a molecular vibration frequency ~ 1012–1013 per second.

If:

kTW=30 to 60

Then:

e−W/kT=e−30 to e−60

which are extremely small numbers.

Plug them in:

τ∼ν−1eW/kT τ∼10−12×e30−60

This yields characteristic event times of thousands of years, which is how Schrödinger arrived at:

Mutation timescale ∼1000−3000 years

He used this to argue that mutations are rare and discrete, leading him to propose the idea of a stable “aperiodic crystal” — what we now know as DNA.

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4. So, How Did Schrödinger Get the Value?

He did not derive it mathematically.
He looked up typical bond activation energies of organic molecules and divided by kT.

Quantity	Value
Activation energy W	0.6–1.2 eV
Thermal energy kT	~0.026 eV
Ratio W/kT	~25–50 (rounded to 30–60)

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