Thermostatistical distribution of a trophic energy proxy with analytical consequences for evolutionary ecology, species coexistence and the maximum entropy formalism

Conventional thermodynamics and statistical mechanics deal with the study of physical systems under equilibrium conditions (EC). Internal EC at a temperature that differs from the environment temperature are sustained, in general, by some type of artificial boundaries imposed with research aims or with quotidian utility goals in many kind of domestic appliances; the typical example of academic lab is a closed system immersed in a thermal bath which keeps the temperature constant. However, the ecosystem is a far-from-EC open system. Therefore, conventional thermodynamics and statistical mechanics tend to be orthodoxly regarded as limited to explain the ecosystem functioning since, at the first glance; there seem to be several essential functional differences between it and the previously-mentioned kind of physical systems. This viewpoint averse to conventional physics is paradoxical in regard to the current ecological paradigm given the fully thermodynamic foundation of ecosystem ecology. However, additional evidence in favor of the usefulness of conventional physics to describe the ecosystem functioning have recently been published, pointing out to the possibility that the analytical approach to ecology based on our undergraduate knowledge of physics, unfortunately, could have been hastily neglected before producing its most valuable results. This paper, fully based on the above-mentioned evidence, performs an unavoidable additional step in order to complete such a proposal by showing that the Boltzmann distribution of molecular energy values can be simply and successfully adapted to model the distribution of values of a proxy for trophic energy across an increasing gradient of energy levels, in a very similar fashion to that of a standard trophic pyramid. Starting from this result and by using a balanced combination between plausible theoretical considerations and abundant empirical data, we analyze why this approach is in agreement with well-known ecological principles, at the same time that we explore the general empirical advantages and aftermaths derived from this suggestion. Finally, the article explores the usefulness of the thermo-statistical modeling of eco-kinetic energy per plot to understand those essential physical factors that: promote biological evolution, facilitate species coexistence, can explain the holes in the fossil record, and enhance our current viewpoint about the ecological meaning of entropy. In summary, this article provides simply understandable additional information that indicates, despite its far-from-EC nature, any natural ecosystem is not far away from the most orthodox principles of conventional physics.