# Negative Changes in Entropy?

## Main Question or Discussion Point

Negative Changes in Entropy??

Perhaps this is not the right forum location, but I would like to ask some of the more experienced physicists here about the notion of negative changes in entropy in the universe. According to the text I am currently reviewing by Hill, the probability that a thermodynamical system will have ΔS<0 is:
$P(\Delta S <0) = {1/(10^{10}}^{20})$

Obviously this is an extremely small number and in our everyday lives we can approximate this as 0. However, on the scale of the universe, are there enough processes that are occurring (or rather, different thermodynamical systems) such that this special case cannot be ignored?

Now assuming such a location in the universe exists where negative changes in entropy can occur, would we see the equivalent of reverse reactions. An example of a reverse reaction would be striking a match in "rewind". This leads me to question several things about physics and our interpretation of the universe (or universes), but I will hold off on those questions for now.

If we assume that no place exists in the universe where negative changes in entopy can occur, does this mean that there is a finite amount of processes that are taking place in the universe, IE are there less than 101020 processes in our universe? Alternatively, is the extremely small value mentioned above simply a mathematical singularity?

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I am kind of surprised nobody has said anything so far... Bad question?

Obviously this is an extremely small number and in our everyday lives we can approximate this as 0. However, on the scale of the universe, are there enough processes that are occurring (or rather, different thermodynamical systems) such that this special case cannot be ignored?
If you are talking at the micro-level, there are lots of examples where you have a temporary local decrease in entropy.

At the level of the observable universe, the answer turns out to be no. You can calculate the chances of something weird happening in something several tens of billions of light years across over several tens of billions of years, and the odds are very low. The observable universe just isn't that large.

Now if the universe were infinite in either space or time, then you'd come up with a different result.

The simplest way to tackle issues in thermodynamics is this: Imagine a system enclosed in a boundary that separates the system from the surroundings. Energy exchanges in the form of heat and work between the system and surroundings are allowed. The second law says that it is impossible for the sum of the entropy changes of the system and surroundings to decrease. However, it is possible for the entropy change of the system to be negative and that of the surroundings to be positive (and vice-versa) so that the their sum is not a negative quantity.
By way of example of negative entropy changes of a system we may quote a simple example:
1. Bring a closed system say, m grams of an ideal gas at a temperature T into thermal contact with a heat reservoir(HR) at temperature T. Allow heat to flow from the system to the HR by reversibly expanding the gas from an initial state of equilibrium A to final state of equilibrium B. Now the entropy change of the system is negative and that of the HR positive their sum being zero. If, instead of HR being at temperature T it is at a temperature less than T, then the expansion of the gas (irreversible) leads to a decrease of entropy of the system and increase of entropy of the HR, the sum being a positive quantity. HR is the surroundings in this example.
Finally, the entropy change at a location in the universe can be negative with a simultaneous entropy change at another location being positive their sum being a non negative quantity, but it is impossible for entropy change at a location to be negative with no other change (or a change that entails the sum of the entropy changes to be a negative quantity) else where in the universe is impossible. The probabilities of the results of these experiments is 1 (100%) with no uncertainties.
Statistical thermodynamics (ST) does not give results that are 100% certain, It gives probabilities of occurrence of processes, such as the one quoted by you, leaving scope to raise questions such as the one you raised. ST results are never 'yes' or 'no' type; while results of (equilibrium) thermodynamics are always 'yes' or 'no' type.

Chronos
Gold Member

That only works if you assume the universe has a boundary. There is no evidence supporting that premise.

If you are talking at the micro-level, there are lots of examples where you have a temporary local decrease in entropy.
Could you describe some examples?

Finally, the entropy change at a location in the universe can be negative with a simultaneous entropy change at another location being positive their sum being a non negative quantity, but it is impossible for entropy change at a location to be negative with no other change (or a change that entails the sum of the entropy changes to be a negative quantity) else where in the universe is impossible.
So would this be an example of Einstein's "Action at at distance"? But again, if you model the universe as a closed system then it is appropriate to ask where the the entropy come from in the first place? In fact, wouldn't it make sense if the net entropy of the universe was zero? While this isn't shown in stat-thermo from a physical perspective wouldnt this imply that the universe is always in equilibrium?

Thanks a lot, the Loschmidt paradox and time symmetry was the exact phenomena I was trying to describe in a not so elegant way.

That only works if you assume the universe has a boundary. There is no evidence supporting that premise.
We don't assume universe has a boundary; we only assume that the system has a boundary. What is not system is surroundings. System and surroundings make the universe.

Chronos
Gold Member

So, you are saying the universe is a system, and, by your logic, it necessarily has a boundary?

So, you are saying the universe is a system, and, by your logic, it necessarily has a boundary?
I wrote, 'System and surroundings make the universe.'

Drakkith
Staff Emeritus

I wrote, 'System and surroundings make the universe.'
I believe the universe as a whole is considered one system, so there would be no surroundings.

I believe the universe as a whole is considered one system, so there would be no surroundings.
If we try to treat the universe as our system it would not help us much. We must then be able to specify its state by giving definite values of the thermodynamic variables such as pressure, volume, temperature, internal energy and so on.

Drakkith
Staff Emeritus

If we try to treat the universe as our system it would not help us much. We must then be able to specify its state by giving definite values of the thermodynamic variables such as pressure, volume, temperature, internal energy and so on.
Why? What's incorrect about not knowing what those variables are?

Not knowing the values of those variables is to confess that we do not know the state of our system.

To get issues in thermodynamics resolved, it is necessary that we have systems in well defined states or else thermodynamics does not give us the results that we seek from it.

Drakkith
Staff Emeritus

Not knowing the values of those variables is to confess that we do not know the state of our system.

To get issues in thermodynamics resolved, it is necessary that we have systems in well defined states or else thermodynamics does not give us the results that we seek from it.
Hold on, can you just define part of the universe to be your system and make it an open system instead of closed?

Hold on, can you just define part of the universe to be your system and make it an open system instead of closed?
We define open system as one in which exchange of matter (besides energy in the form of heat and work) is allowed across the boundary that separates the system and surroundings. To distinguish it from a closed system, we define closed system as one in which exchange energy (in the form of heat and work) is allowed across the boundary that separates the system and surroundings.

Drakkith
Staff Emeritus

Ok, but if you say the system and it's surroundings is the universe, then you can't have anything else outside of this, as the universe isn't believed to have a boundary.

Ok, but if you say the system and it's surroundings is the universe, then you can't have anything else outside of this, as the universe isn't believed to have a boundary.
It is not clear if you have something in mind and trying to drive at it.

Once you define your system then what all that you can imagine or want to have in the universe, can be included in the surroundings. the system and the surroundings now make the universe. You will then be left with nothing more to think of than the universe, which encompasses all that you could think of.

Drakkith
Staff Emeritus

Once you define your system then what all that you can imagine or want to have in the universe, can be included in the surroundings. the system and the surroundings now make the universe.
I'm so confused lol. Ok, all I was saying was that if you have the system AND it's surroundings as the universe, you can't have another boundary somewhere that would be another system and it's surroundings. You could absolutely have part of the universe as the system and the rest as it's surroundings.

Chronos
Gold Member

We define open system as one in which exchange of matter (besides energy in the form of heat and work) is allowed across the boundary that separates the system and surroundings. To distinguish it from a closed system, we define closed system as one in which exchange energy (in the form of heat and work) is allowed across the boundary that separates the system and surroundings.
You have failed to identify what 'boundary' you have in mind that applies to the universe.

I think what he is trying to say is that the you need to define a system inside the universe, where the "universe" is the surroundings. It doesn't really matter if the universe is bounded or not so long as you define a system encompassed by we call the universe because thermodynamics only changes in a system. After-all, aren't all changes relative to something????

An answer to your question lies in the fabric of the replies from your peers. While it can be assumed one could find negative entropy in areas of the universe, it is most obviously not so everywhere. Relativity teaches us that time can be warped by perspective, and as such there are an infinite number of perspectives from which to perceive negative entropy, as long as one understands that at energies/speeds approaching the speed of light that one becomes a source of negative entropy.

Expansion is a huge source of negative entropy, happily subdividing the universe into contained areas.

Very interesting. I really wish I studied physics in undergrad... Do you happen to know of any texts relating to stat-thermo as applied to the universe?

Drakkith
Staff Emeritus