  We consider the thermodynamics of chemical coupling from the viewpoint of
free energy transduction efficiency. In contrast to an external
parameter-driven stochastic energetics setup, the dynamic change of the
equilibrium distribution induced by chemical coupling, adopted, for example, in
biological systems, is inevitably an autonomous process. We found that the
efficiency is bounded by the ratio between the non-symmetric and the
symmetrized Kullback-Leibler distance, which is significantly lower than unity.
Consequences of this low efficiency are demonstrated in the simple two-state
case, which serves as an important minimal model for studying the energetics of
biomolecules.
