May I propose a tiny qualification to this statement? Entropy always refers to transformations of energy -- typically energy's penchant for "speading out" whenever not otherwise restricted (e.g., by boundary conditions or insufficient activation energies). It does not refer to the state of objects after such transformations take place (i.e., the disposition of objects on messy desks or in households for lack of "tidying up." It should be fairly obvious that such "messes" are the result of human failure to keep things neat, not the result of thermodynamic energetic processes).
The trickiest thing about entropy -- and I have been struggling with this concept in recent times -- is that it is a dynamic, real-time process that refers to the distribution of energy between systems (inorganic and organic) and their environment. Statistical analysis can "predict." But actual measurement is a retrospective activity: At the time we measure, the subject system has already "moved on." We can measure its passage; but by the time we do so, only as a "freeze-frame" of some evolution that is already in the past....
A good analogy is a hurricane passing through -- a self-organizing (that is, autocatakinetic) system that draws on both internal and external (environmental) energetic resources in order to exist. The phenomenon of the hurricane as an energetic system is an entirely different matter from the actual physical condition of the debris that it leaves in its wake.
It really is a mind-boggling problem, when the "physical evidence" you have (e.g., debris left in the wake of a past hurricane) that a phenomenon has taken place can tell you nothing about the phenomenon proper (i.e., the hurricane itself), in terms of its actual "disposition of energies." It seems that two categorical orders are involved here.
I need to find better examples to explicate this issue. Will certainly be looking for them.
Then again, maybe I'm "all wet" to begin with! :^)
Thanks for listening to my "rant," A-G!
I'm stumbling over your analysis though because I see the First Law of Thermodynamics being concerned with the transformation of energy whereas the Second Law is concerned with physical entropy.
Then again, I might be just too tired to think (LOL!) I'll literally sleep on it tonight and perhaps I'll be more clear headed tomorrow.
Entropy is not a process. It is a state variable. The entropy of a system depends only on the temperature, pressure, (and other things under some situations) of the system, not on any process involved in creating the system.
Thermodynamically speaking, entropy has the same status as temperature, energy, pressure, etc.
I confess that I do not share your difficulty with the concept, in some measure, perhaps, because I view it mathematically.
Others have discussed entropy as a philosophical concept, and Dr. Stochastic refered to it as a thermodynamic state variable (which it is). However, I prefer to view it from its original derivation in Statistical Mechanics. I always found Thermodynamics hard but Stat Mech easy.
You are indeed correct, that the first law of thermodynamics states that energy is conserved. Therefore, the total heat and work are conserved quantities.
The second law, again you are correct, addresses the distribution of energy.
From its original, mathematical derivation, entropy is indeed a measure of how energy is distributed. It is the natural log of the function omega. Omega is called the density of states function, and gives the total number of quantum states available to the system.
It is also called the partition function, because it defines, essentially, how the energy is partitioned among the various quantum states. In that sense it is usually considered as a distribution function. Indeed, in gas and plasma physics, the derivation is reversed. Assuming a maximum entropy state (i.e. equilibrium), and given a temperature and pressure, you can than calculate the partition of energy among independent, free particles (therefore they do not have discreet quantum states per se). The result is the Maxwellian distribution, which is the three dimensional velocity distribution, or the Boltzmann distribution, which is the 1 dimensional energy distribution. These distributions are the equivalent to the partition function in that they give the distribution of energy among the population of particles. It is a fundamental concept in physics. Systems that are defined as "thermal" are those for which the particle distribution (in energy or velocity) follows the Maxwellian. It is the basis for the thermonuclear bomb and for the definition of temperature.