Microscopic laws vs. Macroscopic laws: Perspectives from kinetic theory and hydrodynamics

Abstract

Reductionism is a prevalent viewpoint in science according to which all physical phenomena can be understood from fundamental laws of physics. Anderson [Science, 177, 393 (1972)], Laughlin and Pines [PNAS, 97, 28 (2000)], and others have countered this viewpoint and argued in favour hierarchical structure of the universe and laws. In this paper we advance the latter perspective by showing that some of the complex flow properties derived using hydrodynamic equations (macroscopic laws) are very difficult, if not impossible, to describe in microscopic framework---kinetic theory. These properties include Kolmogorov's theory of turbulence, turbulence dissipation and diffusion, and dynamic pressure. We also provide several other examples of hierarchical description.