I understand that, in thermodynamics, entropy has a precise definition (the infinitesimal change of entropy being the infinitesimal heat transfer divided by the temperature), and that in statistical mechanics, for a system consisting of a large number of identical subsystems, so to speak, it is the log of the number of possible distributions of the subsystems, corresponding to some given energy levels.
And from what I understand, the Second Law of Thermodynamics basically says that, for some simple systems, such as two reservoirs at different temperatures, connected to each other (and isolated from the rest), heat goes from hot to cold, so that the fact that the entropy wants to be as big as possibly can, is similar to systems going towards an equilibrium state (at least for simple systems such as the one above).
(Please forgive me if my descriptions here are not so accurate from a physical point of view, for I am not a physicist, just a mathematician.)
Fine. But I frequently see people linking entropy to chaos. I assume there is some scientific work which started this train of thought, and then the media kept stretching the words further and further. Can someone please point me to that scientific work? Also, is the link between entropy and chaos valid, in the eyes of modern physicists?
I have seen a few questions that overlap with mine, but I have not found the exact answer to my question.