Emergent Entropic Thermodynamic Force

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:
[tex]F \Delta x = T \Delta S[/tex]
Where F is emergent force and T is black body temperature and S is thermodynamic entropy.

Quantum thermodynamic constant:
[tex]C_1 = \frac{\hbar}{2 \pi c k_B}[/tex]
Where [itex]k_B[/itex] is Boltzmann constant.

Thermodynamic entropy:
[tex]\Delta S = \frac{m \Delta x}{C_1}[/tex]

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

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

Newton's second law:
[tex]\boxed{F = mg}[/tex]

Is there any validity to these equations?

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