Does the Second Law of Thermodynamics Apply to Cosmology?

[TrickyDicky]

Since the second law of thermodynamics builds upon the first, if the first law doesn't apply to cosmology like it keeps being repeated around here, it would seem to follow that that the second law doesn't apply either.
Could this be clarified by someone tat actually knows about cosmology (like Chalnoth or bapowell)?

 

[Drakkith]

What about the 1st law doesn't apply to cosmology?

 

[bcrowell]

What about the 1st law doesn't apply to cosmology?

https://www.physicsforums.com/showthread.php?t=506985

Since the second law of thermodynamics builds upon the first, if the first law doesn't apply to cosmology like it keeps being repeated around here, it would seem to follow that that the second law doesn't apply either.

Why would it follow?

The first law doesn't apply. The second law does.

 

[Chalnoth]

The second law of thermodynamics is generally understood today to be a fundamental rule based upon simple probability: systems tend towards more probable configurations with time. This really isn't a rule that you can get rid of.

 

[TrickyDicky]

The first law doesn't apply. The second law does.

The second law of thermodynamics is generally understood today to be a fundamental rule based upon simple probability: systems tend towards more probable configurations with time. This really isn't a rule that you can get rid of.

Hmm, doesn't the second law rely on the existence of an invariant quantity (energy) to postulate another quantity that increases whenever there is flow from Work to Heat?.
Such a process implies time.
As the energy-time uncertainty principle shows, to measure energy variation a unidirectional passage of time is needed. The variation of heat (dQ) produced in such process fulfills at all times the first law dU=dQ+dW in order for the quantity dS=dQ/T to hold, and also for the non-usable work to end up increasing the internal energy of the system (adiabatic process) or also the internal energy of the surroundings of the system:T\Delta S_u .

This is not contradicted by the "more probable configuration" view of entropy. Why would you consider the firs law an easier law to get rid than the second if thay are both two sides of the same coin?

It is precisely nature's strife to keep with energy conservation book-keeping that ensures that all processes that involve time as a parameter tend to the more probable configuration (the one that keeps energy constant).
As this seems quite basic thermodynamics stuff, I would think that if there's an error in what I wrote it'll be easily spotted and indicated. It seems necessary to straighten this out in order to go back to the issue in cosmology.

 

[Drakkith]

I don't see how energy NOT being conserved has any affect on whether or not systems will tend towards a more probable configuration.

 

[TrickyDicky]

I don't see how energy NOT being conserved has any affect on whether or not systems will tend towards a more probable configuration.

Because if energy wasn't conserved, that is if energy could be created or destroyed and therefore perpetuum mobiles were possible, no configuration would be more probable than others, no gradients or potentials would need to be minimized so energy is conserved since no gradients would form (remember energy is free if it is not conserved), there couldn't be an absolute scale of temperature (no zeroth law) either.
If you are curious as to why once there is energy conservation systems tend to the more probable configuration (since in this case configurations have different probabilities) that is purely semantic, the laws of thermodynamics give you a direction arrow, then we simply call the end point of the arrow "more probable" and the beginning of the arrow less probable, it wouldn't make any difference for the physics if we named them the other way around.

 

[bcrowell]

Hmm, doesn't the second law rely on the existence of an invariant quantity (energy) to postulate another quantity that increases whenever there is flow from Work to Heat?.

No, you can just define entropy in terms of the number of accessible states.

As the energy-time uncertainty principle shows, to measure energy variation a unidirectional passage of time is needed.

Huh? I don't see how any of this has anything to do with quantum-mechanics. We don't have a theory of quantum gravity, so we can't even discuss this quantum-mechanically.

There is no big mystery or controversy about any of this. The first law doesn't hold, and the second law is typically believed to hold. You don't have to trust me on this. For the statement that the first law fails, see the cosmology FAQ entry I linked to above and the references therein. The validity of the second law is pretty much universally assumed, as you can see from even a casual look at the literature. So if you think there is some trivial contradiction there, then you clearly are disagreeing with every cosmologist in the business. It's great if you want to ask probing questions about the conventional wisdom in the field, but if you're proposing that the conventional wisdom is wrong for trivial reasons, then the outcome is going to be that you're going to learn why your reasons are wrong, because people working in the field are not morons.

 

[TrickyDicky]

No, you can just define entropy in terms of the number of accessible states.

Certainly, and as I explained the fact that in an isolated system in which a thermodynamic constrain is removed has more accessible states can be explained in terms of conservation of the internal energy of the system.

Huh? I don't see how any of this has anything to do with quantum-mechanics. We don't have a theory of quantum gravity, so we can't even discuss this quantum-mechanically.

I specified in a previous post that it would be interesting to clarify first the thermodynamical issue of the inseparability of the thermodynamics laws. If this is not the place to discuss it, I'm open to move it to other subforums.
I hope you'll agree there is a theory of quantum thermodynamics.

There is no big mystery or controversy about any of this. The first law doesn't hold, and the second law is typically believed to hold. You don't have to trust me on this. For the statement that the first law fails, see the cosmology FAQ entry I linked to above and the references therein. The validity of the second law is pretty much universally assumed, as you can see from even a casual look at the literature. So if you think there is some trivial contradiction there, then you clearly are disagreeing with every cosmologist in the business. It's great if you want to ask probing questions about the conventional wisdom in the field, but if you're proposing that the conventional wisdom is wrong for trivial reasons, then the outcome is going to be that you're going to learn why your reasons are wrong, because people working in the field are not morons.

Obviously I'm not proposing such thing but your mentioning it leads me to suspect you are just avoiding the physical issue.

 

[Drakkith]

Because if energy wasn't conserved, that is if energy could be created or destroyed and therefore perpetuum mobiles were possible, no configuration would be more probable than others, no gradients or potentials would need to be minimized so energy is conserved since no gradients would form (remember energy is free if it is not conserved), there couldn't be an absolute scale of temperature (no zeroth law) either.
If you are curious as to why once there is energy conservation systems tend to the more probable configuration (since in this case configurations have different probabilities) that is purely semantic, the laws of thermodynamics give you a direction arrow, then we simply call the end point of the arrow "more probable" and the beginning of the arrow less probable, it wouldn't make any difference for the physics if we named them the other way around.

I see no reason that most of this should be true. In my view using my limited knowledge of the subject, a system in equilibium with another system that suddenly acquires more energy would still tend to evolve towards the new equilibrium. Your view seems to be based on the 2nd law NOT being true.

 

[Chalnoth]

Certainly, and as I explained the fact that in an isolated system in which a thermodynamic constrain is removed has more accessible states can be explained in terms of conservation of the internal energy of the system.

The "number of microstates" view is completely independent of considerations related to energy.

 

[TrickyDicky]

The "number of microstates" view is completely independent of considerations related to energy.

So you keep repeating but without further clarification it is either misleading or wrong.
If what you mean is that absolute entropy of a system at a given time is dependent only on the probability of the microstates, without energy entering the formula, that's correct.
Note that absolute entropy at a given time doesn't inform us about the process in time nor gives any unidirectional flow or dynamical picture which is the core of the second law.
And microstates don't come out of the blue, they have a physical meaning. Besides a probability of being occupied they have an energy. And the mean of the sistem's energy is the internal energy which must be conserved in order to measure non negative variation of entropy in spontaneous processes.

 

[Chalnoth]

So you keep repeating but without further clarification it is either misleading or wrong.
If what you mean is that absolute entropy of a system at a given time is dependent only on the probability of the microstates, without energy entering the formula, that's correct.
Note that absolute entropy at a given time doesn't inform us about the process in time nor gives any unidirectional flow or dynamical picture which is the core of the second law.
And microstates don't come out of the blue, they have a physical meaning. Besides a probability of being occupied they have an energy. And the mean of the sistem's energy is the internal energy which must be conserved in order to measure non negative variation of entropy in spontaneous processes.

While it is true that you can decrease the entropy of a system by pumping energy into it, non-decreasing entropy is still taken to be more fundamental than energy conservation.

Quantum effects, like the ones you mentioned, do not impact this argument because they tend to average out, producing no net change in energy.

Gravity is more difficult to factor in, because gravity breaks the assumptions that go into classical thermodynamics. So the relationships we make use of in thermodynamics are not expected to hold except in special cases where the gravitational entropy is either negligible or isn't changing. Furthermore, energy isn't always conserved in General Relativity (it is conserved in special cases).

 

[TrickyDicky]

While it is true that you can decrease the entropy of a system by pumping energy into it, non-decreasing entropy is still taken to be more fundamental than energy conservation.

Why? They're both parts of the same process, I don't understand why one is taken to be more fundamental than the other.
It's like saying that in the sales process of a product is more fundamental the buying than the selling, it is just dependent on whose POV is used , the buyer's or the seller's.
Instead of entropy we could equally choose to use Free-energy=internal energy-unusable (T\Delta S) energy, which is a form of using an energy dynamic measure (free energy decreases the same way entropy increases) for instance when using Gibbs or Helmholtz free energy.
According to WP : "Free energy is that portion of any first-law energy that is available to perform thermodynamic work; i.e., work mediated by thermal energy. Free energy is subject to irreversible loss in the course of such work. Since first-law energy is always conserved, it is evident that free energy is an expendable, second-law kind of energy that can perform work within finite amounts of time."
It is evident from this that the second and first law are inextricably interconnected, it makes little sense considering one more fundamental than the other except for special applications.
And makes no sense at all to claim one law holds and the other doesn't, since they are each based on the other holding true.

Quantum effects, like the ones you mentioned, do not impact this argument because they tend to average out, producing no net change in energy.

Sure, in an equilibrium situation there is no net change of internal energy, this follows from the first law too.

 

[TrickyDicky]

Back to cosmology, judging by the answers I'm getting, it seems clear a choice has been made by "working cosmologists" (and according to the references provided), that when faced between thermodynamics as a logically complete model with all of its laws, and the FLRW model of cosmology as put forward in the 30's of the XXth century , they clearly lean towards the latter.
I guess that is a valid choice if sufficiently supported, but not the only choice possible.
What I don't understand is what kind of arbitrarines allows to cherry pick certain laws of thermodynamics and not others ignoring that thermodynamics is a logically complete whole that includes all of their laws.

 

[Chalnoth]

Why? They're both parts of the same process, I don't understand why one is taken to be more fundamental than the other.

Because entropy is simply related to the number of microstates that can replicate a given macrostate. This means that the second law of thermodynamics is, fundamentally, a statement about probability: systems tend towards higher-probability states.

If you look carefully at what the heat transfer part means in classical thermodynamics you see that this condition is what is required to ensure that global entropy increases. In other words, the heat transfer part of the second law of thermodynamics is peculiar to the classical assumptions used.

Sure, in an equilibrium situation there is no net change of internal energy, this follows from the first law too.

Out of equilibrium as well. Quantum effects simply don't lead to average changes in energy.

 

[TrickyDicky]

Because entropy is simply related to the number of microstates that can replicate a given macrostate. This means that the second law of thermodynamics is, fundamentally, a statement about probability: systems tend towards higher-probability states.

If you look carefully at what the heat transfer part means in classical thermodynamics you see that this condition is what is required to ensure that global entropy increases. In other words, the heat transfer part of the second law of thermodynamics is peculiar to the classical assumptions used.

I'm still not sure whether you consider energy conservation a necessary condition for the second law.
Let's consider as usual isolated systems (the universe is normally considered an isolated system) and it might be useful to differentiate reversible processes from irreversible ones.
So if we consider an isolated system far from equilibrium we have the irreversible case and there is unidirectional time and the second law that states that it'll tend towards more probable configurations with time until it reaches equilibrium.
What happens to the system if we don't impose that dU=0 (first law)? Basically that energy can be created within the system to avoid the gradient that is formed far from equilibrium, IOW an artificial equilibrium can be formed that prevents any more probable configuration to tend to and therefore there is never increase in entropy and dS=0.

Is this wrong?

 

[Chalnoth]

Is this wrong?

The part of the second law of thermodynamics that relates to how a transfer of heat can allow a decrease in entropy assumes energy conservation from the start. If you don't have energy conservation, then this part of the second law would have to be rewritten to take that into account when you have an open system.

However, if I just want to deal with a lack of conservation of energy and don't want to worry too much about how that impacts the behavior of open systems, I can just take a closed system and be sure that the entropy won't decrease. Once the system is closed, the conservation or non-conservation of energy is completely irrelevant. Energy conservation only comes into it when you want to understand the behavior of an open system.

 

[TrickyDicky]

The part of the second law of thermodynamics that relates to how a transfer of heat can allow a decrease in entropy assumes energy conservation from the start. If you don't have energy conservation, then this part of the second law would have to be rewritten to take that into account when you have an open system.

That part of the second law is the only part as it is usually defined.

However, if I just want to deal with a lack of conservation of energy and don't want to worry too much about how that impacts the behavior of open systems, I can just take a closed system and be sure that the entropy won't decrease. Once the system is closed, the conservation or non-conservation of energy is completely irrelevant.

I'm not sure if you are using the standard meaning of "closed system" in thermodynamics (a system that can exchange energy but not matter). In such a system entropy can decrease (like in a refrigerator), remain invariant if no net energy is transferred or increase.
Do you mean that once equilibrium is reached conservation of energy is irrelevant? The fact is all isolated systems in equilibrium trivially conserve energy (they are reversible systems and time symmetric by definition).

Energy conservation only comes into it when you want to understand the behavior of an open system.

To make things simpler and since the universe is considered an isolated system and also most definitions of entropy are made in terms of isolated systems I suggest we stick to isolated systems.

 

[Chalnoth]

I'm not sure if you are using the standard meaning of "closed system" in thermodynamics (a system that can exchange energy but not matter). In such a system entropy can decrease (like in a refrigerator), remain invariant if no net energy is transferred or increase.

Looking it up, I suppose the more accurate term is an isolated system, which has no interaction with the outside world. A refrigerator obviously interacts with the outside world, and couldn't work if it didn't.

 

[TrickyDicky]

So I take it that at least for isolated systems we agree that the second law assumes the first law. (if not, please claify what you ment by "the part of the second law that assumes conservation of energy from the start")

 

[Chalnoth]

So I take it that at least for isolated systems we agree that the second law assumes the first law. (if not, please claify what you ment by "the part of the second law that assumes conservation of energy from the start")

No, absolutely not. For isolated systems, the second law does not need the first law. The first law is only made use of when you allow the system to exchange heat with its environment. If your system is isolated, there is no exchange of heat, and we don't need to worry about the first law at all. We can just rely upon the fundamental definition of entropy as the logarithm of the number of microstates that replicate the given macrostate, and from that definition it is easily proven that entropy will (almost) never decrease.

If you didn't have energy conservation, then you still might be able to write something similar to the second law for systems where heat is exchanged, but you would need to take into account the specific way in which energy isn't conserved.

 

[TrickyDicky]

No, absolutely not. For isolated systems, the second law does not need the first law. The first law is only made use of when you allow the system to exchange heat with its environment. If your system is isolated, there is no exchange of heat, and we don't need to worry about the first law at all.

But then you didn't really answered to my post #17 with your #18, I made it clear I was talking about isolated systems.
Can you refute my explanation in #17?

 

[Chalnoth]

But then you didn't really answered to my post #17 with your #18, I made it clear I was talking about isolated systems.
Can you refute my explanation in #17?

You're mixing laws where the behavior of matter conserves energy with a rule that there is extra heat input into the system. That's not an isolated system. Nor is it a valid thing to do.

 

[TrickyDicky]

You're mixing laws where the behavior of matter conserves energy with a rule that there is extra heat input into the system. That's not an isolated system. Nor is it a valid thing to do.

That's exactly my point, thanks, you are highlighting the need for the first law, it isn't a valid thing to do as long as the first law holds, if it doesn't apply is perfectly valid, since energy is not a conserved quantity you can create energy in an isolated system.

 

[Chalnoth]

That's exactly my point, thanks, you are highlighting the need for the first law, it isn't a valid thing to do as long as the first law holds, if it doesn't apply is perfectly valid, since energy is not a conserved quantity you can create energy in an isolated system.

But that has nothing to do with the second law and how it can be made to apply to systems where energy isn't conserved.

 

[TrickyDicky]

But that has nothing to do with the second law and how it can be made to apply to systems where energy isn't conserved.

My claim is that in that case it can't be made to apply and in what I set up dS is always zero, I'm not sure if that is compatible with the second law, maybe it is since the law states dS= or >0

 

[Chalnoth]

My claim is that in that case it can't be made to apply and in what I set up dS is always zero, I'm not sure if that is compatible with the second law, maybe it is since the law states dS= or >0

dS=0 is a perfectly valid possibility for the second law in an isolated system.

But as I keep trying to say, the non-decreasing rule of entropy can be trivially derived for any isolated system given the definition of entropy. Various conservation laws simply don't come into it. The only assumptions being made here are that we can define certain macroscopic variables to describe the behavior of the system, and that we can count the number of configurations that correspond to each possible set of macroscopic variables. That is all that comes into the proof.

Now, bear in mind that if you loosen the various conservation laws, you may end up with a system that increases in entropy indefinitely. But you won't end up with a system that routinely lowers in entropy.