The Second Law of Thermodynamics is intimately linked to the thermodynamics of the breakdown of glucose. By "the thermodynamics of the breakdown of glucose," I mean: is the breakdown of glucose spontaneous, is it thermodynamically favorable?
You may have seen the criteria for the thermodynamic favorability of a reaction in terms of Gibbs Free Energy:
$$\Delta G = \Delta H - T\Delta S\leq0$$
That is, for a reaction to be favorable, the change in Gibbs free energy from the initial state (glucose) to the final state (carbon dioxide, water, and energy) must be negative. This equation is valid for systems at constant temperature and pressure, which is assumed to be satisfied in biological systems. According to Wikipedia, $\Delta G$ for the breakdown of glucose is negative, $\Delta G = -2880$ kJ/mol.
However, there is a nice derivation on Wikipedia that the above equation is nothing more than a statement of the second law of thermodynamics, applied to the case of constant temperature and pressure. So in sum, the second law of thermodynamics is the reason that glucose can be broken down in such a way that useful energy is released in the form of ATP, i.e. that the reaction is spontaneous or thermodynamically favorable. Saying that the Gibbs Free Energy of the breakdown products is lower than that of glucose itself is the same as saying that the breakdown of glucose does not decrease the total entropy of the reaction and its environment.