New concept for quantification of similarity relates entropy and energy of objects: First and Second Law entangled, equivalence of temperature and time proposed

Abstract

When the difference between changes in energy and entropy at a given temperature is correlated with the ratio between the same changes in energy and entropy at zero average free energy of an ensemble of similar but distinct molecule-sized objects, a highly significant linear dependence results from which a relationship between energy and entropy is derived and the degree of similarity between the distinctly different members within the group of objects can be quantified. This fundamental energy-entropy relationship is likely to be of general interest in physics, most notably in particle physics and cosmology. We predict a consistent and testable way of classifying mini black holes, to be generated in future Large Hadron Collider experiments, by their gravitational energy and area entropy. For any isolated universe we propose absolute temperature and absolute time to be equivalent, much in the same way as energy and entropy are for an isolated ensemble of similar objects. According to this principle, the cosmological constant is the squared product of absolute time and absolute temperature. The symmetry break into a time component and a temperature component of the universe takes place when the first irreversible movement occurs owing to a growing accessed total volume.