From an Entropic Measure of Time to Laws of Motion

TL;DR

This paper develops an entropic measure of time leading to a new kinematic law relating system size, particle number, and emergent forces, extending the deductive formulation of physical theories.

Contribution

It introduces a novel entropic measure of time that results in a new kinematic law and explains emergent forces based on system density and size.

Findings

Derived a kinematic law linking time, size, and particle number.

Found accelerated growth and size-dependent particle decrease in systems.

Predicted inverse-square and constant forces based on system density.

Abstract

A hypothesis proposed in the paper (Entropy 2017, 19, 345) on the deductive formulation of a physical theory based on explicitly- and universally-introduced basic concepts is further developed. An entropic measure of time with a number of properties leading to an analog of the Galileo-Einstein relativity principle is considered. Using this measure and a simple model, a kinematic law which relates time to the size and number of particles of a system is obtained. Corollaries of this law are examined. In particular, accelerated growth of the system size is obtained, whereas in systems with constant size decrease in the number of particles is observed. An interesting corollary is the emergence of repulsive and attractive forces inversely proportional to the square of the system size for relatively dense systems and constant for systems with sufficiently low density.