Question

Explain how the internal entropy of a biomolecule can be approximated by S = k ln w

Answer 1

Here, we have introduced Boltzmann's notion of Wahrscheinlichkeit, pronounced var-SHINE-leash-kite, symbol W, which does not seem to have an exact English equivalent but is assumed to be a cross or blend between "probability" and "multiplicity", so to speak, referring to the number of “states” the particles of the system can be found in according to the various energies with which they may each be assigned, in quantum mechanical speak.

To note, if our integral had the form of what is called as an "indefinite integral", one without upper and lower limits, an additive constant would be used:

This version, although it seems we are missing a step in the derivation (somewhere?), seems to be the sense in which Planck first introduced the natural logarithm formulation of entropy in 1901, in his own notation as follows:

and where SN is the entropy of a system or black body composed of N resonators, which, according to Planck, "depends on the disorder with which the total energy U is distributed among the individual resonators. , Planck was calling the following equation, without the added constant, the ‘general definition of entropy’, albeit discussed in his chapter on the equation of state of a monoatomic gas:

Some consider S = k ln W to be easily the second most important formula of physics, next to E = mc² or at par with it.