Emergent Entropic Thermodynamic Force

[Orion1]

I have just watched a video lecture from Robbert Dijkgraaf at Gresham College where he describes gravitation as an emergent entropic thermodynamic force. The video link is listed in reference and the equations are defined at time index 44:00.

Emergent entropic thermodynamic force:
F \Delta x = T \Delta S
Where F is emergent force and T is black body temperature and S is thermodynamic entropy.

Quantum thermodynamic constant:
C_1 = \frac{\hbar}{2 \pi c k_B}
Where k_B is Boltzmann constant.

Thermodynamic entropy:
\Delta S = \frac{m \Delta x}{C_1}

Black-body thermodynamic temperature:
T = C_1 g
Where g is surface gravity acceleration.

Integration via substitution:
F = \frac{T \Delta S}{\Delta x} = \left( \frac{C_1 g}{\Delta x} \right) \left( \frac{m \Delta x}{C_1} \right) = mg

Newton's second law:
\boxed{F = mg}

Is there any validity to these equations?

Reference:
The End of Space and Time? - Professor Robbert Dijkgraaf

 

[jfizzix]

A few questions pop to mind:
What is S the entropy of? (this is very important since apparently 1-D thermodynamics is maybe being used to describe a 3D system here?)
Where do the third and fourth equations come from?

Without solid answers to these questions, no sensible conclusions can be made out of this string of math.

Hoping this helps:)