Small and simple systems that favor the arrow of time

The 2nd law of thermodynamics yields an irreversible increase in entropy until thermal equilibrium is achieved. This irreversible increase is often assumed to require large and complex systems to emerge from the reversible microscopic laws of physics. We test this assumption using simulations and theory of a 1D ring of N Ising spins coupled to an explicit heat bath of N Einstein oscillators. The exact entropy of the spins and bath can be calculated for any N, with dynamics that is readily altered from reversible to irreversible. We find thermal equilibrium behavior in the thermodynamic limit, and in systems as small as N=2, but only if the microscopic dynamics is intrinsically irreversible.