In class, I discussed the concept of spontaneous reactions and free energy in qualitative terms. However, a number of you answered using some ideas and equations from other classes, so I thought I should connect what I said with these other approaches. Otherwise, there is quite a bit of room for confusion. On the midterm, I accepted anything close to correct, without splitting hairs.
The one overall, humongous principle is that things occur when there is a net increase in entropy, taking all interconnected parts into account. This applies to physical processes and chemical reactions alike. It is how the universe is put together. Diffusion from a high concentration to a low concentration is the most basic example.
In physiology, we are only concerned with chemical reactions that occur at constant temperature, since they occur in the body. Thus, the following explanation only pertains to this case. For a specific chemical reaction, you need to consider two things. The first is the actual reacting system of molecules. For example, when glucose reacts with oxygen to form carbon dioxide and water, the reacting system consists of the molecules themselves. The second factor is the environment surrounding these molecules. This is important because heat is given up to this environment during the reaction of the molecules.
As the reaction occurs, the overall entropy change is equal to the sum of the entropy change of the surrounding environment and the entropy change of the reacting system of molecules. In mathematical terms, this is given as ΔG = ΔH - T ΔS.
ΔG is the free energy change. It directly indicates the overall entropy change. ΔH is the heat given to the environment. It is negative if heat is given by the system of molecules to the environment. This implies an increase in entropy since the potential energy in a molecule like glucose is being converted to random, thermal motions in the environment. T is equal to the temperature. ΔS is the entropy of the reacting system of molecules. In biology, the entropy of the system is positive mainly if there is an increased number of molecules. Note that heat given to the environment tends to make ΔG negative, and increased entropy of the system tends to make ΔG negative.
In almost all reactions in the body, the ΔH is much larger than the TΔS. Thus, saying that a reaction is spontaneous if "heat is given off by the reaction" is pretty close to correct. Also, notice that the ΔS term is not the overall entropy, but only the small entropy change in the reacting system of molecules itself. It is the ΔG that indicates the overall entropy change, since it is determined by the sum of the two components.