Pressure as an Entropic Force

PΔV = TΔS

The Gas Law can be cast in this form.

PV = NkT

if ΔS = Nk

N is the number of particles, and k is Boltzmann's constant.

This law can be derived from Newton's Second Law of motion, if one averages, and multiplies it by Δx, to get rid of time. Conceptually one says that a particle does not have temperature nor pressure. They are emergent qualities of the thing, i.e., we think of pressure and temperature as a substitute for force and kinetic energy of a single particle. Something like life insurance companies do not care if I die or live, they only care if the average number of people dying produces a profit, when compared with the living ones that pay their monthly fees.

It is the law of big numbers at play. Pascal, Fermat, and Gauss, come to mind. We cannot say if a wager is a win or a loss, we can only say that around half of the coin tosses will be tails, and half heads.

How could Gravity be Entropic?