The Constructal law and its place in thermodynamics

Every law of physics is a concise statement that addresses a phenomenon occurring in nature. The Structural Law was born of the realization that the concept of "design" is a universal physical phenomenon covering extremely broad domains and extremely different scales, from the dendritic shape of a snowflake to the watershed of the Amazon. Its principle was established in 1996 . This law is at the origin of a body of work that represents a new extension of thermodynamics: the thermodynamics of non-equilibrium systems with configuration and evolution.

Let's imagine an isolated thermodynamic system in an initial internal state of non-uniformity, such as subdomains at different pressures or temperatures separated by an internal wall that suddenly breaks. The first and second laws of thermodynamics take into account observations that describe a trend over time: given enough time, the isolated system tends towards a new state of equilibrium: no internal currents, entropy becomes maximum at constant energy. The first and second laws describe a black box. Nothing is said about the evolution of the configuration (design, architecture) of the flows concerned.

Classical thermodynamics is not concerned with the configurations of these non-equilibrium flow systems. Yet it should be. Indeed, Sadi Carnot's memoir deals with improving configurations over time. His intuition was shared by many who sought to increase thermodynamic performance in different fields (engineering, biology, geophysics, economics...) without perceiving the universality of their approach: generating configurations over time to optimize thermodynamic efficiency.

This tendency, a temporal sequence of new designs, new forms that the system possesses as it evolves, is the phenomenon covered by the Construct law; not the design itself, but the direction in time towards which the system evolves if it has the freedom to do so.

According to the Constructal Law, the generation of flow patterns in nature and in engineering obeys an identical principle. Nature and engineering can each be approached in two ways, either empirically or theoretically. On the one hand, observing nature in order to copy it comes first and serves as a starting point for modeling, description and bio-inspired engineering. The Constructal approach runs counter to this: flow architecture is deduced from the Constructal law. Only then is the theoretical configuration compared with an equivalent configuration found in nature.