  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.
