One problem with this argument is the earth is not a
closed system. Another is, biological complexity is 
not the same type as any sort of complexity that would
 be relevant when talking about thermodynamics. Allow 
me to explain.

The second law of thermodynamics is not in conflict with
the theory of evolution. The sun pumps out a lot of energy.
A small percentage of this energy is used by plants to make
sugar via photosynthesis. From there, energy flows through
the food web. For the solar system there is a net increase
in entropy (and it's not even closed).

No extra energy other than that derived from photosynthesis
is needed for populations to evolve. Evolution is a change
in the gene pool of a population over time. Several mechanisms
can bring about evolutionary change, they are: natural selection,
genetic drift, mutation, recombination and gene flow.

Natural selection is differential reproductive success of
genetic variants in the gene pool. This requires no "extra"
energy other than the energy the organisms obtain from
photosynthesis (either directly or indirectly).

Genetic drift is a binomial sampling error of the gene
pool. In other words, each generation is a sample of genes
from the previous generation's gene pool. In a finite
population, gene frequencies change slightly each generation
due to chance. Again, no "extra" energy is needed to fuel
evolution.

Mutation is a change in a gene. This can be caused by
DNA replication errors or by damage due to radiation. Once
again, no conflict with the second law of thermo (although
the energy to cause the mutation does not come from photosythesis
in the case of radiation damage.)

Recombination is exchange of genetic information
(usually) with sister chromatids or homologous chromosomes. The
enzymes that accomplish this work do so with energy derived from
photosynthesis (again, either directly or indirectly). Once again,
no conflict with thermodynamics.

And finally gene flow is migration of new genes into a
population. This often occurs by fertile hybrids "bridging"
two gene pools. No thermodynamic problems here.