  We show that there is a class of stochastic baker's transformations that is
equivalent to the class of equilibrium solutions of two-dimensional spin
systems with finite interaction. The construction is such that the equilibrium
distribution of the spin lattice is identical to the invariant measure in the
corresponding baker's transformation. We also find that the entropy of the spin
system is up to a constant equal to the rate of entropy production in the
corresponding stochastic baker's transformation. We illustrate the equivalence
by deriving two stochastic baker's maps representing the Ising model at a
temperature above and below the critical temperature, respectively. We
calculate the invariant measure of the stochastic baker's transformation
numerically. The equivalence is demonstrated by finding that the free energy in
the baker system is in agreement with analytic results of the two-dimensional
Ising model.
