Use and Abuse of Entropy in Biology: A Case for Caliber

Abstract

Here, I discuss entropy and its use as a tool in fields of biology such as bioenergetics, ecology, and evolutionary biology. Statistical entropy concepts including Shannon’s diversity, configurational entropy, and informational entropy are discussed in connection to their use in describing the diversity, heterogeneity, and spatial patterning of biological systems. The use of entropy as a measure of biological complexity is also discussed, and I explore the extension of thermodynamic entropy principles to open, nonequilibrium systems operating in finite time. I conclude with suggestions for use of caliber, a metric similar to entropy but for time-dependent trajectories rather than static distributions, and propose the complementary notion of path information.

Interdependent Autonomous Human–Machine Systems: The Complementarity of Fitness, Vulnerability and Evolution

“…Entropy is a thermodynamic quantity in a system that reduces the system’s available energy to perform useful work [ 39 ]. We will argue that the structure (the configuration, the skills and roles of team members, etc.)…”

“…From the discussion, we next assume that the ability of a team to be productive is related to its ability to minimize the team’s configuration entropy produced by its structure [ 46 ]. We show that achieving minimal or the least entropy production through a team’s structure (SEP), as suggested by Equations (4) and (5), allows a team to direct more of its available free energy to increasing its productivity [ 39 ], possibly even to achieve maximum entropy production (MEP; [ 19 ]). An example of MEP would be a highly productive team, e.g., a marriage devoted to raising its children; a business such as Apple Technology Company becoming ever more productive in its struggle to reach MEP based on its structure; an alliance devoting all of its available free energy to solving the problems placed before it; or a nation’s people educated to search through potential solution spaces to solve the problems faced by a nation with solutions that can be patented [ 52 ].…”

Entropy Perspectives of Molecular and Evolutionary Biology

“…This would imply the paradox that during the evolution of living beings the entropy of biomass decreases, in contrast to the second principle of thermodynamics. The paradox appears from the ambiguous, when not arbitrary, identification of organization and complexity with low entropy and high information, and of entropy with disorder [34][35][36]. Then, information-based models of organisms propose that evolution is associated to increased organism diversity and entropy of ecosystems [37][38][39], higher entropy production [40,41] and, often, that entropy production would be maximized in fully evolved enzymes [42].…”

Statistical Physics of Evolving Systems

“…Rather, it is a struggle for entropy that becomes available through the flow of energy from the hot sun to the cold earth" [1]. Despite Boltzmann's insight [2,3], the relationship between increasing entropy and decreasing free energy has remained obscure [4]. Early on, Carnot understood that a change in entropy, dS = δQ/T, follows from a change in energy δQ per temperature T (i.e., average energy when multiplied with Boltzmann constant k B ).…”