Entropy
Entropy is a measure of the disorder of a system, and there is a greater probability that any system will be in a disordered, rather than an ordered, system. (last word should have been "state" -- TT)
It is common enough to equate entropy & disorder, but I don't think that's right.
Entropy is something we can objectively define & calculate, whereas
disorder is an entirely subjective concept which is not consistently defined and cannot be calculated. It's easy to think of entropy as "disorder" when dealing with something where we have common ideas of "order" (all the billiard balls in a triangle ready for the break) or "disorder" (all the billiard balls scattered around the table). But whether or not the high probability state of a system is "disordered" is not objective, and especially so if we are dealing with non-equilibrium systems. The habit of matching entropy with order/disorder is what allows creationists, for instance, to argue (falsely of course) about the impossibility of order arising from disorder as a proof for the impossibility of evolution.
I prefer to avoid the order/disorder business and retreat to the objective mathematics. Simply put,
entropy is what the equations say it is. So, in classical thermodynamics (which deals with statistically very large numbers of particles), the entropy (
S) for a system at a give temperature is
S = Q/T where
Q is the total heat energy content of the system and
T is its temperature. In an equilibrium system where the temperature does not change, then the change in entropy (
∆S) is easy enough to define:
∆S =∆Q/T. It's just a ratio of heat energy to temperature, and surely there is no sign of "order" and "disorder" in this classical view of entropy.
The transition to statistical mechanics is where probability, and the resultant appeal to order & disorder come into play. In this case the entropy for a system is defined as
S = -k·[Pilog(Pi)], where
Pi is the probability that particle "i" will be in a given microstate (that's the physical state of the particle itself), and all of the
Pi are computed for the same macrostate (that's the average physical state of the entire system of particles; temperature for instance, which is related to the average kinetic energy of the particles that make up the system). If all of the microstate probabilities are the same, then that equation reduces to the simpler (and more commonly shown) equation
S = k·log(Ω), where
Ω is the total number of microstates which can result in the observed macrostate (i.e., how many ways are there to distribute kinetic energy over the particles of a system, such that they all result in the same temperature). Clearly
Ω can be a huge number. (k is just Boltzmann's constant, 1.380658x10
-23 Joules/Kelvin).
The statistical equations, unlike the classical equations, do not explicitly include either heat energy content or temperature. Nevertheless, the requirement that all of the particle microstate probabilities must be calculated for the same system macrostate ensure that the system must be in thermal equilibrium. So if you want to try dealing with entropy in a non-equilibrium system, you can't use the simplified equation, you have to use the equation that deals explicitly with individual particle probabilities.
As it turns out, one can show that the definitions of entropy from classical thermodynamics and statistical mechanics really amount to the same thing (but this is a non trivial exercise left for the student
). Note that the popular level correspondence between entropy and disorder makes sense only in the statistical description, but is certainly not apparent in the classical description. This is not surprising, since classical thermodynamics deals only with properties averaged over extremely large numbers of discrete particles (temperature, pressure, volume & etc.), whereas statistical mechanics deals explicitly with the discrete particles. It is somewhat remarkable, really, that these two regimes of physics generate the same conclusions give the same physical system.
Hopefully this is not too mathematical to deal with so far, but I do it to emphasize my own point:
Entropy is what the equations say it is. Forget about order, disorder, or anything else. The equations tell you what entropy is and they are in fact the definitive authority on the topic. And this is true throughout all of physics. If you want to know what
X really is, go first to the equations and let them lead the way, not somebody's prosaic description. This is really necessary when dealing with topics like quantum mechanics, or relativity, where there are few handy concepts laying around, like order or disorder, that one can use to create an useful analogy. This is one of the reasons why the "alternative thinkers" we deal with in these fora almost always fail; they try to use words and skirt the equations, as if mathematics is somehow a foul means of understanding what's happening, when in reality it may well be the only means of understanding what's happening.
Now, moving on, the second law of thermodynamics, in classical thermodynamics, tells us that heat will not
spontaneously flow from lower temperature to higher temperature systems (but of course refrigerators are not impossible because they are not spontaneous). An equivalent statement in both classical & statistical thermodynamics is that the entropy of a
thermodynamically isolated system (sometimes described simply as "closed") will never decrease, but rather can remain constant or increase (the latter being more likely). But as Sol Invictus has already told us, the argument is entirely probabilistic despite being called a "law". It's just that the probability of the law being violated is so low we can easily ignore it (but one should always bear in mind that "improbable" and "impossible" are
never synonymous). Boltzmann's original derivation of all this is (or at least was) still in print thanks the the Dover Reprint series,
Lectures on Gas Theory. Otherwise, I find the old classics
The Principles of Statistical Mechanics by Richard C. Tolman, or
Statistical Physics by Gregory H. Wannier to be most useful references.
