Relativity, thermodynamics and entropic forces

Abstract

A recent assertion that inertial and gravitational forces are entropic forces is discussed. A more conventional approach is stressed herein, whereby entropy is treated as a result of relative motion between observers in different frames of reference. It is demonstrated that the entropy associated with inertial and gravitational forces is dependent upon the well known lapse function of general relativity. An interpretation of the temperature and entropy of an accelerating body is then developed, and used to relate the entropic force to Newton's second law of motion. The entropic force is also derived in general coordinates. An expression of the gravitational entropy of in-falling matter is then derived by way of Schwarzschild coordinates. As a final consideration, the entropy of a weakly gravitating matter distribution is shown to be proportional to the self-energy and the stress-energy-momentum content of the matter distribution.