Robert Batterman, Pittsburgh :: Explaining Autonomy: Mesoscale Models and Many-Body Systems
Friday March 15, 2024

Abstract: Many-body systems often display different behaviors at different scales. The behavior of a fluid flowing past an obstacle is adequately captured by the continuum Navier-Stokes equations.  But its behavior at molecular and atomic scales are not well-modeled using continuum equations. It is remarkable that the continuum equations work at all, as they posit no structure below the continuum scale. How can one explain the (relative) autonomy of the continuum equations from the "more fundamental" lowest scale physics?  I argue that to understand this autonomy, it is essential to appeal to mesoscale structures.  Various parameters appearing in continuum models are best understood as coding for such mesoscale structures.  I draw some philosophical lessons about how to think about natural properties and minimal model idealizations.