Two nanoparticles connected by a polymer will tend to be drawn together at finite temperatures (though not at absolute zero) because as the polymer chain explores the states available to it, there are many more tangled and balled up ones than stretched-out straight ones — even though there is no overt force pulling the chain to any particular tangled state. Such a situation is called an entropic spring, and behaviors like this are some of the more interesting aspects of physics at the microscale.

An arXiv paper by physicist Erik P. Verlinde purports to show that gravitational effects have the same mathematical logic behind them (in a very broad analogical sense), arising from the holographic universe description of physics (a far-out variant of string theory). Now I don’t come close to having the physics to evaluate the theory, but Verlinde appears to be a respectable physicist. Czech physicist Luboš Motl blogged about it:

So I remain undecided whether or not there is a sharp insight waiting along the lines of Verlinde’s paper.

and then allowed Verlinde to guest-post a long explanatory comment.

The derivation of the Einstein equations (and of Newton’s law in the earlier sections) follows very similar reasonings that exist in the literature, in particular Jacobson’s. The connection with entropy and thermodynamics is made also there. But in those previous works it is not clear WHY gravity has anything to do with entropy. No explanation for this apparent connection between gravity and entropy has been given anywhere in the literature. I mean not the precise details, even the reason why there should be such a connection in the first place was not understood. My paper is the first that gives a reason why. Inertia, and hence motion, is due to an entropic force when space is emergent. This is new, and the essential point. This means one HAS TO keep track of the amount of information. Differences in this amount of information is precisely what makes one frame an inertial frame, and another a non-inertial frame. Information causes motion.

This can be derived without assuming Newtonian mechanics.

“Space is emergent”??? Yep, in the holographic theory, 3D space is an emergent phenomenon of a 2D information pattern (see the link above). Weird stuff, but no weirder than other forms of string theory.

As mentioned, I don’t claim to follow this at the technical level, but given how important the math of entropy is at the microscale, it’s fun to speculate about its being important at the most macro of macroscales as well.