Is the concept of entropy a result of limited technology?

Question

I know that entropy is the energy within a system that is unable to do useful work. However, there was a time in which we were unable to harness the energy of the wind or the sun, and now we can, using turbines and solar panels. Is the energy that is lost to entropy really lost? It still exists, due to the conservation of energy, and thus must be accessible via some sort of technology.

If I recall correctly, entropy can also be described as the dispersion of energy within a system. This can be proved true via the following chain of logical assumptions:

1. Entropy in the universe is always increasing, overall.
2. The end state of the universe, under current models, is a thin sea of subatomic particles.
3. Thus, a thin sea of subatomic particles has high entropy.

While mankind will be long dead before the heat death, it would in theory be possible to harness the energy of these particles, even if it would take far more energy to extract it than it would give out. However, it would be possible nonetheless.

In conclusion, is entropy merely a result of our technological limitations?

Answer 1

I know that entropy is the energy within a system that is unable to do useful work.

This doesn’t really bear scrutiny. Entropy and energy have different units, for one. But even an approximate analogy would be in trouble: A hotter object has a greater entropy, and it would also provide more work if I connected it to a heat engine (in conjunction with a cold reservoir). So the comparison doesn’t really make intuitive or rigorous sense.

Here’s one better way to think about it: If you ask me to obtain work from a fast-moving cold object or a hot motionless object with the same total energy, I’ll take the moving object every time. The reason is that I can extract all the kinetic energy of the cold object by bringing it to a complete halt. But I can never extract all the thermal energy from the hot object because I have no such “wall”—that is, I have nothing at absolute zero that I can let the hot object heat (while inserting a heat engine to extract work). At best, I can let the hot object heat something around me at room temperature, and this isn’t as efficient. (In particular, if the hot object is at room temperature, its thermal energy is useless to me.)

I didn’t mention entropy at all in the previous example, but it can be completely understood through an entropy framework. Specifically, the (1) hotter object has greater entropy, and (2) heat transfer is entropy transfer, broadly inversely proportional to the temperature, and (3) entropy can’t be destroyed. So the engineering limitation is a matter of maximizing the temperature difference we can provide to the heat engine. In this context, we are indeed limited by our technology (e.g., the need for refractory and creep-resistant moving engine parts that can withstand great heat).

The way you “harness at least some of the energy locked in entropy,” as you put it, is to find the largest, coldest cold reservoir you can to drive and maintain the greatest possible heat transfer. But asking whether we can completely sidestep Carnot constraints, for example, is to ask whether we can perform heat transfer without performing heat transfer—it’s just a nonstarter.

Answer 2

Totally wrong. Entropy is NOT "the energy within a system that is unable to do useful work." Instead entropy is the thermal charge that does work as it moves from a higher temperature to a lower temperature the same way as a piece of mass when lowered from higher gravitational potential to a lower gravitational potential or an electric charge is moved from a higher electric potential to a lower electric potential, etc.

Answer 3

I'll address the "limited technology" part of the question. To begin with the specific "brand" of entropy being dealt with here is that having to do with the operation of heat engines.

Over the last 140 years or so, the first-principle underpinnings of heat engine physics have been completely worked out from theory (in at least two completely different ways), compared with reality, and proven thereby to accurately represent the real-life operation of heat engines of every basic sort. The practice of heat engine physics is called thermodynamics and has its own fundamental laws. In this (general) sense, thermodynamics as as applied to heat engine design represents a solved problem.

This means that thermodynamics contains no "wiggle room" in which fundamental breakthroughs (that would require rewriting those laws) can possibly take place. This means that there's no technological way around the laws of thermodynamics that contain expressions for entropy. We are well and truly stuck with them.

In fact the only way those laws allow the real-life practice of thermodynamics to exhibit advances as our technology improves is through the invention of materials from which we construct our heat engines that support their operation at higher and higher temperatures- which permits them to show better and better efficiencies within the mathematical framework of the laws of thermodynamics.

Answer 4

The problem is that entropy is a process of probability. There is no fundamental force that can be exploited that causes entropy to increase all the time. Entropy increases simply because it is overwhelmingly, statistically, more likely than a decrease in entropy. How much more likely it is truly cannot even be expressed. If you don't already know why this is the case, but you want to understand, then read on pass this paragraph. If you want the (really) short summary, then here: In order to defy the Second Law of Thermodynamics with technology, you'd need to create a device that is able to defy basic probability on a fundamental level.

If you're still reading, then buckle up. While the whole "Entropy is a measure of disorder" is a good starting point and is easy to grasp, it's not really correct. If you want a better, more accurate definition of entropy, here's one: "Entropy is a measure of the probability of a systems properties." That definition alone will give you a better understanding of the concept of entropy than 95% of the world population. An even better definition is "Entropy is a measure of the number of possible microstates that correspond with a system's given macrostate."

Microstates are states of a system that are concerned with the properties of each individual variable. Macrostates are states that are concerned with only the systems overall properties. Macrostates are determined by microstates. In classical statistical mechanics, all microstates are equally likely. However, not all macrostates are equally likely.

To show what I mean, I want you to imagine that you have a pair of six sided die. The die are completely fair, meaning for both die, each number has exactly a 1 in 6 chance of landing face up. We will also label the die as "Dice A" and "Dice B" to assist in our understanding of microstates. Now as previously mentioned, but slightly reworded, microstates are the combination of individual properties of the variables within a system. So the microstate of a rolled pair or group of die is the exact numbers that appear on each individual dice. If you roll a pair die, likes the ones that have been labeled "Dice A" and "Dice B", there are 34 possible microstates. They are as follows:

"A-1" "B-1"; "A-2" "B-1"; "A-3" "B-1"; "A-4" "B-1"; "A-5" "B-1"; "A-6" "B-1"; "A-1" "B-2"; "A-1" "B-3"; "A-1" "B-4"; "A-1" "B-5"; "A-1" "B-6"; "A-2" "B-2"; "A-3" "B-2"; "A-4" "B-2"; "A-5" "B-2"; "A-6" "B-2"; "A-2" "B-3"; "A-2" "B-4"; "A-2" "B-5"; "A-2" "B-6"; "A-3" "B-3"; "A-4" "B-3"; "A-5" "B-3"; "A-6" "B-3"; "A-3" "B-4"; "A-3" "B-5"; "A-3" "B-6"; "A-4" "B-4"; "A-5" "B-4"; "A-6" "B-4"; "A-5" "B-5"; "A-6" "B-5"; "A-5" "B-6"; "A-6" "B-6"

Now remember, for these die, and for classical statistical mechanics, all of these microstates have an equal probability of occurring. You are just as likely to roll "A-5" "B-2" as you are likely to roll "A-3" "B-1". 1 in 34 chance for both.

Now what about macrostates? What determines those? The microstates do. A macrostate is simply a broader, or more general view of a systems overall properties, defined by the combined or averaged properties of all the variables. All possible microstates have a corresponding macrostate and all possible macrostates have at least one corresponding microstate. Notice how I said "at least one". The reason why not all macrostates are equally likely is because different macrostates have different amounts of corresponding microstates. Macrostates with more corresponding microstates are more likely to occur than macrostates with less corresponding microstates. If you're having trouble understanding, then hopefully returning to the die analogy will help.

For the die, the sum of all the numbers of each die rolled can be seen as a macrostate. For two die, there are 11 possible macrostates: 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12. If I were to ask you which number is most likely to be rolled, you could probably tell me, either by doing the math and figuring it out, or because of all the experience you gained from playing monopoly on friday nights with the family. The most likely number is, of course, seven. And it's easy to understand why. Seven has six possible microstates that all correspond with it: "A-1" "B-6"; "A-6" "B-1"; "A-2" "B-5"; "A-5" "B-2"; "A-3" "B-4"; and "A-4" "B-3". In fact, seven is six times more likely to occur than twelve and two, because those numbers both only have one macrostate each that correspond with it: "A-1" "B-1" for two, and "A-6" "B-6" for twelve.

But you may or may not be thinking "But those both still have a 1/34 chance of occurring. It's not likely, but it's far from being nearly statistically impossible like you say decreasing entropy is." And you'd be right. But if you were thinking that, which you probably weren't, but I digress, then you forgot to account for one thing: The number of variables.

What if we increase the number of die from 2 to 100. There are now far many more microstates relative to macrostates. While there are now 501 macrostates, there are now also 6^100, or 6.5x10^77, or approximately 650,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 microstates. Despite this, both of the macrostates 600 and 100 have only one microstate each, meaning if you roll all 100 die at the same time, the odds of rolling 600 or 100, are 1/650,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. The most likely number to roll, in contrast, is 350, which has roughly a 2% chance of occuring. Those odds may seem small, which they are, but all other macrostates are exponentially less likely than that even.

Now hopefully you can begin to see why we never see a spontaneous decrease in entropy. If 100 variables with only 6 possible properties each can result in such staggeringly improbable statistics, now imagine what we've just talked about on the macro scale, with atoms, molecules and other particles being the individual variables. A simple glass of water has roughly 6x10^24 molecules. Each one of those molecules is a variable and each variable has an incredibly wide array of properties, such as kinetic energy, position, velocity, quanta stored, etc. To reiterate what I said in the first paragraph: If you want defy the Second Law of Thermodynamics using technology, you would somehow have to be able to invent a device capable of bypassing statistics and probability itself.