Energy and information: a chronicle of hesitations on the role of the observer in physics

Abstract

Energy has no definition, except that given by a conservation principle which essentially amounts to defining it as the elements of an open list of unknown cardinality. Entropy, identified by Shannon as information we lack, has too many definitions. This results in an unstable and hesitant interpretation of their link. Thermodynamics, the science of changes in form of energy, is phenomenological, all its laws are induced from observation. From the origin, the concept of energy is linked to the observer's knowledge, to the information he has: what and where to look and with what instruments. Thermodynamics only addresses the sensible world. It is Aristotelian. But this is disturbing if we consider that reason can give us access to Plato's intelligible world, the one that is beyond the sensible world and independent of us. This is disturbing if we consider that science can access to the intrinsic properties of things, those which are independent of us. This is disturbing if we have a purely Platonic conception of science. Hence the statistical mechanics approach ("The rational foundation of thermodynamics", J.W. Gibbs). This is the first pendulum movement of ideas, whose oscillations continue to this day, because unfortunately statistical mechanics introduces many inconsistencies, mainly due to the ergodic hypothesis. Luckily, these inconsistencies are all solved by Shannon's information theory. Sadly, information theory is too Aristotelian and too conceptual. Fortunately, Landauer principle makes it more \textquote{physical}. This is currently the latest attempt to bringing the notions of energy and information back to what is considered the right side of science, that of Plato. Landauer principle is now commonly regarded as a fundamental law of physics. Unpleasantly, it can be shown that this principle is not one.