EDIT: Look -- if you don't understand physics, don't compound your ignorance by downvoting the posts of people who do. Instead, post a written objection, and I will explain why you're wrong.
I like to consider ∆S the result of a smoothing operation over energy differentials.
You can put work into a system to reestablish an energy differential. It just necessitates obtaining that other energy differential with which to do the work.
> I don't like that definition.
Physics isn't a popularity contest.
http://en.wikipedia.org/wiki/Entropy
> You can put work into a system to reestablish an energy differential.
Yes, but that doesn't change the definition of entropy -- it just borrows energy from somewhere else.
Why link me to the Wikipedia article or insinuate I'm pulling this out of--to put it more politely--ex culo? Given my use of notation, one might assume I am at least a little familiar with how the thermodynamic entropy functions are mathematically derived.
To be pedantic for a bit, Entropy is an abstract mathematical state function useful for the prediction of thermodynamic systems. Much like the Gibbs and Helmholtz terms, entropy has no direct qualitative basis; there are many open-ended interpretations seeking to justify what it means, which is not unlike looking for God or faeries or what have you.
Mathematically speaking, I think you got your equality / definition wrong. Which energy function do you refer to? If you are still convinced about an error on my part, you can demonstrate in classical thermodynamics that,
S = "the inverse of available energy to do anything"
What's my incentive to continue a discussion with someone who has abandoned the topic? In a closed system, the amount of exploitable energy, and the quantity called entropy, move in opposite directions.
> ... or insinuate I'm pulling this out of--to put it more politely--ex culo?
Point to where I said this. If you can't, then you have abandoned the topic.
> Much like the Gibbs and Helmholtz terms, entropy has no direct qualitative basis; there are many open-ended interpretations seeking to justify what it means, which is not unlike looking for God or faeries or what have you.
Nonsense. Entropy is clearly understood, it's not a philosophical puzzle as you suggest. It's easily quantifiable. It's science, not philosophy.
> Given my use of notation, one might assume I am at least a little familiar with how the thermodynamic entropy functions are mathematically derived.
Anyone can adopt the notations used in science. This doesn't tell me anything about their knowledge of the topics under discussion. You simultaneously apply standard terminology, but you go on to say that explaining entropy is "not unlike looking for God or faeries or what have you", which means you don't understand the significance of the symbols you used.
Entropy = k log(n)
k = Boltzmann's constant.
n = number of states the system can be in.
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/temper2.ht...
Quote: "Temperature is expressed as the inverse of the rate of change of entropy with internal energy, with volume V and number of particles N held constant. This is certainly not as intuitive as molecular kinetic energy, but in thermodynamic applications it is more reliable and more general."
Yeah, but physics aren't a la carte. Either prove it wrong (and get a nobel) or accept it.
Okay, here's a commonly used explanation. Entropy and time are bound together -- as time passes, overall entropy increases (with local violations like us). This is one idea about why time "moves" in the direction it does -- if time were to reverse, we could tell because some classic entropy results would run in reverse, violating common sense.
Imagine that there's a room, and in one corner of the room there's a perfume bottle. At time zero, the cork is removed from the perfume bottle. Because of entropy, the tendency of isolated systems to move from order to disorder, the perfume disperses through the room.
Ask yourself what the probability is for the perfume to spontaneously recombine in the bottle, versus the probability that it will disperse through the room. That probability differential is a measure of entropy.
> So is there somewhere in universe some energy that is not available to do anything at all?
Sure -- any isolated system can eventually get to a point where no useful work can be performed. Imagine an engine without any temperature differentials anywhere, or any way to acquire a temperature differential from an external source. Such an engine cannot do useful work.
A steam engine requires a heat source and a heat sink. Without a temperature differential, the engine cannot function. Same with a gas engine.
> Is it too diffuse such that the energy needed to pull it together to perform a unit of work is greater than the energy available ?
But without tapping an external energy source, the energy in an isolated system won't concentrate itself or spontaneously create a temperature differential suitable for exploitation. In an isolated system, the level of disorder always increases over time.
> If so how did it get to that state?
Simple physics. For two masses having a temperature difference, one with temperature "a", the other "b", and a temperature conductivity of "k", they will eventually reach the same temperature this way:
Δ = (b-a) e^(-t k)
Δ (delta) = temperature difference at time t
a = temperature a
b = temperature b
t = time
k = energy transfer coefficient
As an aside, this is my own pet theory as to why some actions of living beings seem to resist scientific prediction. Observed within its own boundaries, a living being appears to be a system that locally decreases entropy; therefore within those boundaries it does not appear to operate causally.
So for example we can predict a human being who is deprived of food will die (basic energy balance), but we can't use science to predict what color shirt they will choose to wear next Tuesday.