Quantum-theoretic Shapes of Constituents of Systems in Various States

Abstract

In previous publications, it has been shown that entropy is a measure of the quantum-theoretic shape of the constituents of a system. In this paper, we present examples of quantum-theoretic shapes of some systems each consisting of one unit of a single constituent, in either a stable (thermodynamic) equilibrium state or in states that are not stable equilibrium. The systems that we consider are a structureless particle confined in either a linear box or a square box, and a harmonic oscillator. In general, we find that the shape of each constituent is “smooth”—without ripples—for each thermodynamic equilibrium state, and oscillatory or rippled for states that are either nonequilibrium or unstable equilibrium.