Modified Newtonian Dynamics as an entropic force
  Under natural assumptions on the thermodynamic properties of space and time
with the holographic principle we reproduce a MOND-like behaviour of gravity on
particular scales of mass and length, where Newtonian gravity requires a
modification or extension if no dark matter component is introduced in the
description of gravitational phenomena. The result is directly obtained with
the assumption that a fundamental constant of nature with dimensions of
acceleration needs to be introduced into gravitational interactions. This in
turn allows for modifications or extensions of the equipartion law and/or the
holographic principle. In other words, MOND-like phenomenology can be
reproduced when appropriate generalised concepts at the thermodynamical level
of space and/or at the holographic principle are introduced. Thermodynamical
modifications are reflected in extensions to the equipartition law which occur
when the temperature of the system drops below a critical value, equals to
Unruh's temperature evaluated at the acceleration constant scale introduced for
the description of the gravitational phenomena. Our calculations extend the
ones by Verlinde (2011) in which Newtonian gravity is shown to be an emergent
phenomenon, and together with it reinforces the idea that gravity at all scales
is emergent.
