  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.
