  Discovery of a novel thermodynamic aspect of nonrelativistic gravity is
reported. Here, initially, an unspecified scalar field potential is considered
and treated not as an externally applied field but as a thermodynamic variable
on an equal footing with the fluid variables. It is shown that the second law
of thermodynamics imposes a stringent constraint on the field, and, quite
remarkably, the allowable field turns out to be only of gravity. The resulting
field equation for the gravitational potential derived from the analysis of the
entropy production rate contains a dissipative term due to irreversibility. It
is found that the system relaxes to the conventional theory of Newtonian
gravity up to a certain spatial scale, whereas on the larger scale there
emerges non-Newtonian gravity described by a nonlinear field equation
containing a single coefficient. A comment is made on an estimation of the
coefficient that has its origin in the thermodynamic property of the system.
