The Equivalence of Free Energy and Information: Thermodynamic Descriptions as a Condition of Possibility of Objectivity

Abstract

The natural world is composed of dynamic forms of physical order over a wide range of length, time, and energy scales. Furthermore, these various forms of physical order form nested hierarchies in which certain processes are logically dependent on the stability of other processes. Over the past century, extensive labor has gone into theorizing about this complexity, and in pursuit of a satisfactory mathematical definition of “complexity.” At the same time, philosophical debate over “emergence vs reductionism” has ossified into well-trodden positions that lack any clear relationship to the mathematical and physical developments on the subject. The aim of this work is to present the advancements in physics over the past few decades, along with the proper meaning of the concept of information in statistical physics, in such a way that the significance of these developments to the traditional philosophical debate on emergence and reductionism becomes manifest. Our view is that the scaling requirements of thermodynamic descriptions should be understood as conditions of the possibility of being “objective” about a situation at a given scale, and thus identifies the natural scales of emergence for those objects. Several well-understood examples such as the relationship between the entropy and the structure of biological macromolecules and the ordered phases of fluids will be discussed. Next, we will illustrate both the proper meaning of entropy in classical thermodynamics and its relationship to Shannon information theory, demonstrating that free energy can be understood as a measure of information exchanged between a system and its environment. The correspondence of free energy and information in turn sets the stage for a more self-aware use of language in recognizing the implicit scaling limits that come with addressing the natural world at multiple scales simultaneously.