In Gibbs free energy, entropy is treated as a sort of energy. The increase of entropy can generate work and release energy. However, normally energies are associated with actual forces. Light is due to electromagnetic force, potential energy due to attractions/repulsions in fundemental forces. Air Pressure is a force that generates potential energy by atoms crashing into boundaries. Is entropy associated with any physical force?
No. Entropy transfer is associated with non-work energy transfer (aka heat transfer). The driving force for heat transfer is a temperature difference. On a more fundamental level, entropy generation within a system is associated with dissipation of useable energy as a result of finite driving forces for heat transfer (temperature gradients), momentum transfer (velocity gradients), mass transfer (concentration gradients), and chemical reactions (chemical potential differences).
I am going to talk about internal energy in this answer rather than Gibb's free enegy. It is simply a more natural setting for the qustion you are asking.
The way thermodynamics treats entropy is closer to the way it treats volume than the way it treats energy. I can change the energy of a system by changing its volume (I typically do work on the system to compress it and it does work when it expands) but that does not mean that volume is a type on energy. How much the energy changes when I compress the volume depends on the force of the system resisting that compression, that is the pressure.
Entropy works in a largely analogous way. I can change the entropy of a sytem by heating it, which also increates the energy of the system. How much the energy changes for a given change in entropy (the quantity analogous to pressure in the case of volume) is the temperature (in fact this is often taken as the definition of temperature).