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The considerable impact of Verlinde’s recent paper in which he suggests that gravity is nothing but anentropic forcehas familiarised many with this type of force.

Verlinde wrote:

The examples he mentions involve constituents in thermal equilibrium with a fluid heat An entropic force is an effective macroscopic force that originates in a system with many degrees of freedom by the statistical tendency to increase its entropy. The force equation is expressed in terms of entropy differences, and is independent of the details of the microscopic dynamics. In particular, there is no fundamental field associated

with an entropic force. Entropic forces occur typically in macroscopic systems such as

in colloid or bio-physics. Big colloid molecules suspended in an thermal environment

of smaller particles, for instance, experience entropic forces due to excluded volume

effects. Osmosis is another phenomenon driven by an entropic force. Perhaps the best

known example is the elasticity of a polymer molecule. A single polymer molecule can

be modeled by joining together many monomers of fixed length, where each monomer

can freely rotate around the points of attachment and direct itself in any spatial

direction. Each of these configurations has the same energy. When the polymer

molecule is immersed into a heat bath, it likes to put itself into a randomly coiled

configuration since these are entropically favored. There are many more such

configurations when the molecule is short compared to when it is stretched into an

extended configuration. The statistical tendency to return to a maximal entropy state

translates into a macroscopic force, in this case the elastic force.

bath: a uniform liquid or, in the case of pressure --- also an entropic force --- a uniform

ideal gas.

In cosmology, the LCDM model is based on thecosmological principlethat we are not

in any way specially situated in the universe. The model assumes that the universe’s

uniformly expanding spatial geometry is that of a homogeneous and isotropic everywhere gravitating cosmic fluid whose dynamics are ruled by general relativity. At first glance, therefore, gravity as an entropic force fits well into this scheme, based on a model fluid.

But the universe is not quite uniform. Wiltshire,

while discussing the modifications that he argues should be made to the perceived age of the universe and the perceived acceleration of expansion ---- because of inhomogeneities --- notes that:

I find puzzling the concept of gravity being treated as the same entropic force both in empty voids and deep inside galaxies, and get confused in trying to identifying the nature Wiltshire said:At the present epoch.... following the growth of complex structures from gravitational collapse, the universe is only statistically homogeneous if sampled on large scales of order 150–300 Mpc. A box of the size of statistical homogeneity may be as small as 100h−1 Mpc, where h is the dimensionless parameter related to the Hubble constant by H0 = 100h km sec−1 Mpc−1. .....If we include the numerous minivoids of smaller diameters, then the volume of thepresent universe is dominated by empty voids, while clusters of galaxies are spreadin a cosmic web of bubble-like sheets that surround the voids, and thin filaments that thread them.

of the heat bath which validates calling gravity an entropic force. Does the CMB perhaps act as a heat bath for gravity? And is there evidence that Newton's law of gravity (which Verlinde derives) is the same deep inside voids as it is deep inside galaxies?

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# Entropic gravity and cosmology

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