Order and Chaos in the One-Dimensional $φ^4$ Model : N-Dependence and the Second Law of Thermodynamics

William Graham Hoover, Kenichiro Aoki

Published 2016-05-25Version 1

We revisit the equilibrium one-dimensional $\phi^4$ model from the dynamical systems point of view. We find an infinite number of periodic orbits which are computationally stable while at the same time exhibiting positive Lyapunov exponents. We formulate a standard initial condition for the investigation of the microcanonical chaotic number dependence of the model. We speculate on the uniqueness of the model's chaotic sea and on the connection of such collections of deterministic and time-reversible states to the Second Law of Thermodynamics.