  We consider various modeling levels for spatially homogeneous chemical
reaction systems, namely the chemical master equation, the chemical Langevin
dynamics, and the reaction-rate equation. Throughout we restrict our study to
the case where the microscopic system satisfies the detailed-balance condition.
The latter allows us to enrich the systems with a gradient structure, i.e. the
evolution is given by a gradient-flow equation. We present the arising links
between the associated gradient structures that are driven by the relative
entropy of the detailed-balance steady state. The limit of large volumes is
studied in the sense of evolutionary $\Gamma$-convergence of gradient flows.
Moreover, we use the gradient structures to derive hybrid models for coupling
different modeling levels.
