A Philosophical Investigation of Entropy

            If entropy is just a statistical fact about a system, why is it often described as something that is being created, generated, or transferred in a thermodynamic context? Quite simply, the reason for this is because it is convenient to think of entropy in those terms. We often use heat and energy as physical quantities that are put into and out of a system, so it is easy to think of entropy in that same way. But I think it would be a mistake to define entropy as chaos or disorder, but should instead be described in terms of possible states. Instead of saying that a system has generated x amounts of disorder, it would be more accurate to say that the number of possible states of a system has increased, just as it would be better to say that there is an increase in kinetic energy in an object rather than saying that an object generated kinetic energy. I often hear that entropy is a difficult concept to understand and that it is mysterious, but when you look at entropy in terms of usefulness, I don't believe it to be the case. I am not saying that the amount of entropy in a system is easy to calculate, or that I even necessarily understand entropy, I am just saying that entropy seems to be simple concept at the heart of it.

            From doing this web project, I thought of some interesting ideas concerning entropy. Zero entropy is defined as a system with only one possible state (so a system of particles arrayed in a perfect crystalline lattice at zero Kelvin would satisfy this condition). If entropy has constantly been increasing, there is a finite time in the past when entropy was zero because it makes no sense to have negative entropy. If this is the case, this is evidence for the Big Bang because you can only reach an entropy value of zero when the entire universe is a singularity. However, it is also possible that entropy approaches zero but never actually reaches it. This gives us a paradox in that an increase in temperature gives us an increase in entropy and it is extremely hot as we approach the Big Bang.

            On another note, the entropy of a black hole and at the boundary of the universe must be infinite because we cannot know its possible statistical configurations.  But maybe what I am referring to is informational entropy rather than thermodynamic entropy. Hawking and Bekenstein gave us a formula for calculating the entropy of a black hole but the problem I have with their formula is that they only account for the area of the event horizon, and I understand this is to account for the increase of entropy due to mass, but this does not take into consideration all the degrees of freedom for every particle entering the black hole. If entropy were simply a function of mass, then entropy would not increase with an increase in temperature. Also, how many degrees of freedom do we assign to a single unit of dark matter that enters a black hole? To me, it makes no sense to even attempt to calculate the entropy of a black hole when its possible states are impossible to determine.