  Lyapunov exponents of a dynamical system are a useful tool to gauge the
stability and complexity of the system. This paper offers a definition of
Lyapunov exponents for a sequence of free linear operators. The definition is
based on the concept of the extended Fuglede-Kadison determinant. We establish
the existence of Lyapunov exponents, derive formulas for their calculation, and
show that Lyapunov exponents of free variables are additive with respect to
operator product. We illustrate these results using an example of free
operators whose singular values are distributed by the Marchenko-Pastur law,
and relate this example to C. M. Newman's "triangle" law for the distribution
of Lyapunov exponents of large random matrices with independent Gaussian
entries. As an interesting by-product of our results, we derive a relation
between the extended Fuglede-Kadison determinant and Voiculescu's S-transform.
