# Does the concept of entropy become redundant over an infinite time scale?

An example of entropy I found was:

"A campfire is an example of entropy. The solid wood burns and becomes ash, smoke and gases, all of which spread energy outwards more easily than the solid fuel."

Let's say burning this campfire takes an hour, yes the entropy has increased over this time scale as the wood is now converted into gas, smoke and ash etc. Order to disorder.

Over time the materials left will then be incorporated into the soil and atmosphere, from which ordered things grow such as plants from the soil which use the gas from the atmosphere. So in the short term 1 hour after the fire the entropy has increased, but after tens of thousands of years the order returns. So you could only say the increase in entropy occurs in a certain time scale?

On a larger scale:

"Like all stars, our Sun radiates away its concentrated energy, increasing its entropy, and slowly coming into equilibrium with the cold vacuum of space."

So let's say the sun takes 10 billion years to burn out. Over that time scale the entropy has increased.

However stars form by:

"Stars form by the slow contraction under gravity of a very large cloud of gas and dust particles in space."

So over a vast time scale the atoms that the sun released will be used again to form new stars?

Therefore if the system you were considering has an infinite amount of time, then is it correct to say there is no true movement from order to disorder, as the order returns given enough time.

• Pretty much all concepts will be redundant on an infinite time scale. Dec 14, 2022 at 0:34
• Quibble: the remnants of the camp-fire will never be as ordered as they were when they were wood. Those atoms became wood through (a complicated process made possible by) energy. If those atoms form something else that's more ordered, it requires energy. It's conceivable (if you burn them in a closed system) to have most of them go into wood or whatever other ordered product you wish, but they won't have the same order - entropy still wins. Dec 14, 2022 at 0:47

Over time the materials left will then be incorporated into the soil and atmosphere, from which ordered things grow such as plants from the soil which use the gas from the atmosphere. So in the short term 1 hour after the fire the entropy has increased, but after tens of thousands of years the order returns. So you could only say the increase in entropy occurs in a certain time scale?

You are thinking locally, not globally. Yes, if you have a tree, cut it down, burn it, and then somehow later all of the particles that had been in the tree end up making the same exact tree later, then the tree particles end up in exactly the same state as it had been before it was cut down (this is assuming the tree is "static" of course; a gross oversimplification).

However, in order for this to happen, the entropy of everything else would have increased. This is a common misunderstanding of the second law of thermodynamics. It doesn't say the entropy of every system increases, nor does it say that the entropy of every system can never decrease. Certainly there are many processes that decrease the entropy of a system. The key in the second law is that a system must be isolated. Only then can we say the entropy can never decrease for that system. In your case the tree particles do not constitute a closed system, so the second law doesn't apply to the tree particles on their own.

So in the short term 1 hour after the fire the entropy has increased, but after tens of thousands of years the order returns

Second law of thermodynamics does not forbid entropy decrease or staying constant in general,- it is allowed if system is not isolated and it has energy in-flow.

For example our bodies maintains same level of entropy due to lasting metabolism : eating food- taking energy from outside of our bodies, fixing cells, replacing them, removing toxic waste, etc. After death, metabolism stops, hence entropy starts to build-up in an organism. (Actually entropy starts to build-up sooner, that's why we are prone to aging,- because not all errors in an organism can be fixed, and many of them - accumulates).

What second thermodynamics law actually says is :

The entropy of isolated systems left to spontaneous evolution cannot decrease

So you fail to notice that plants (trees and the like), which "maintains order",- does that using photosynthesis,- getting energy from our Sun. It's not that situation is left for "spontaneous evolution",- it does not.

Spontaneous evolution is when you are not washing your dirty plate(s) and see that over time dirty cluster of plates increases. That's what 2-end law of thermodynamics speaks about.

This is a very good question, and the answer is No. Using Conservation of Energy (i.e. 1st Law of Thermodynamics) alone, ordered systems can indeed arise out of disordered ones. E.g. ice cubes could melt into lukewarm water in a glass, and then reform into ice cubes and hotter water. The law of entropy increase (2nd Law of Thermodynamics) is a separate concept required to explain the evolution of a system.

The best way I've found to characterize entropy is matter and energy mixing and spreading out.

For instance, in your campfire example, the gases (CO2 and H2O) that once made up the log are dispersed and mixed into the atmosphere (N2,O2) and diluted to undetectable levels. Gathering the CO2 molecules from amongst the N2 and O2 requires energy input $$E_{in}$$. I.e. a process or being must discriminate between CO2 and other molecules. Plants do this via photosynthesis, but this requires energy from the Sun. And the energy required to collect 1 log's worth of carbon from the atmosphere is more than the energy that was released by burning the log ($$E_{log}$$).

So to return to the state of having an unburned log with stored energy $$E_{log}$$ ready to be ignited, it requires the following energy to be expended:

$$E_{return}=E_{log}+E_{in}$$

Where $$E_{in}$$ accounts for photosynthesis, a human being cutting the log and lifting it over to the campfire area, etc.

The important point is $$E_{return}$$ will always be greater than $$E_{log}$$, the energy released by the process in the forward direction.

In addition, what enabled the plants to perform the unmixing of carbon from air was the energy $$E_{sun}$$ received from the sun. But the total amount of $$E_{sun}$$ needed to collect 1 log's worth of carbon is greater than the $$E_{log}$$ released by burning the log.

So at every step in the energy usage process, it requires more energy to return to the previous state as is liberated by getting to the current state.

The basic reason for this, again, is mixing and spreading out, which I find more helpful to visualize than "disorder." Examples of processes that increase entropy are: alcohol being poured into water, CO2 gas mixing with air, a pressurized gas venting out of a container and escaping (position states mixing), a hot object cooling into a cooler environment (thermal energy states mixing), an ordered Ace-King deck of cards being shuffled by a dealer. Try to imagine "undoing" any one of these processes. They can all be done, but in every case, it requires a person or a machine to actively expend effort distilling the alcohol, collecting the gas, pumping out the heat, or choosing and ordering the cards one by one. This extra effort must itself come from an entropy-increasing process (i.e. a process that causes some part of the universe to become more mixed and spread out than it was). Therefore, total entropy of the universe must always increase.

On an arbitrarily long time scale as you mention, we have what is called the Heat Death of the universe. All stars will burn out, any object hotter than the vacuum of space (2 Kelvin) will cool to 2 Kelvin, and we will be left with cold matter and light waves. Nothing interesting will happen anymore, because all thermal and physical states will be maximally "spread out" and "mixed," and no usable energy source will be available to "unmix" them. The universe will be like a wind-up toy that has completely wound down.

Here is a short video series that may be of interest, which gives a brilliant overview of this topic.