Approximate Embeddings in Statistical Mechanics

Abstract

It is part of the scientific folklore of industrial societies that macroscopic systems like gases and solids, stars, tables and animals are “composed of” atoms and molecules. Most of us are so accustomed to this atomistic view that we tend to overlook the conceptual problems inherent in the expression “composed of”. On second thought we are faced with two incommensurable views of the same individual systems: For example, when we use the microscopic description of a gas in terms of many atoms we are unable to say what the temperature of the gas at a given spatial point is. (Most of the time there won’t even be a single atom near that point.) On the other hand, when using a macroscopic (thermodynamic) description it is impossible to say where all the particles are. Yet there must be an intimate connection between the two descriptions: For example we are able to identify the substance “water” either by its macroscopic properties (density, viscosity, freezing and melting points etc.) or by the structure of its molecules (H₂O).