  We show that the thermodynamic entropy density is proportional to the largest
Lyapunov ex- ponent (LLE) of a discrete hydrodynamical system, a deterministic
two-dimensional lattice gas automaton. The definition of the LLE for cellular
automata is based on the concept of Boolean derivatives and is formally
equivalent to that of continuous dynamical systems. This relation is jus-
tified using a Markovian model. In an irreversible process with an initial
density difference between both halves of the system, we find that Boltzmann's
H function is linearly related to the expansion factor of the LLE, although the
latter is more sensitive to the presence of traveling waves.
