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# Second Law of Thermodynamics

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But would this equation still hold if the universe contracted?

The Universe can't contract acording to second law. So this equation is applied in the second law. If ∆S is negative, Sgen will be negative and become impossible state. The Universe will exhaust and isentropically stop and equal entropy!

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Anyone want to interject here with some word definitions of entropy. I believe that one must look at the system. I believe the controversy here revolves around the definitions of entropy and an expanding universe, which I believe are used in a cyclical definition. No time to look it up right now, if no one else does in the next 8 hours, I'll be back.

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The formula for entropy is:

delta S = n* R *ln(Vf/Vi)

I think this formula derives from Boltzmann’s principle (S=k*ln(M)), where k is Boltzmann’s constant, M (usually written omega) is an integer representing the number of possible microstates of the system, and is only appropriate to apply to an ideal gas in thermodynamic equilibrium.

For the universe, with its varied small and large structures and uneven mass/energy distribution, I think M is many orders of magnitude smaller than it would be if the entire universe were an ideal gas at equilibrium. Thus the substitution of Vf/Vi for M is not appropriate, so the volume of the universe is not strongly related to its entropy.

Because of the large difference between the universe’s effective M and the maximum it could be (eg: if it really was a homogenous, ideal gas of fundamental particles), I don’t believe the 2nd Law prohibits the volume of the universe from contracting.

There are many strong arguments against the possibility of the universe contracting (eg: an closed, oscillating or “big crunch” model), most of which say something about the universe not having enough gravitational interaction to halt its expansion. I don’t believe, however, that an argument based on the 2nd Law of Thermodynamics is among them, except possibly at the point in a big crunch scenario that the universe is compressed into a very small volume. Perhaps, then, Thermodynamics argues that

• a gravitationally closed universe cannot crunch into less than a certain volume, rather like an the closed oscillations in volume of a globular cluster; or
• only a small portion of the universe – its fermion and massive bosons, perhaps – can be gravitationally closed, allowing a lot of information/disorder to escape as bosons (radiation); or
• when a contracting big crunch universe reaches a certain volume, time really does begin running backwards

I strongly doubt the last of these is possible. For all its beauty and utility, thermodynamics is really just a collection of statistical laws, describing the exceeding likely, but not the absolutely possible. If “push came to crunch”, I suspect quantum mechanical law would trump thermodynamic.

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I think this formula derives from Boltzmann’s principle (S=k*ln(M)), where k is Boltzmann’s constant, M (usually written omega) is an integer representing the number of possible microstates of the system, and is only appropriate to apply to an ideal gas in thermodynamic equilibrium.

For the universe, with its varied small and large structures and uneven mass/energy distribution, I think M is many orders of magnitude smaller than it would be if the entire universe were an ideal gas at equilibrium. Thus the substitution of Vf/Vi for M is not appropriate, so the volume of the universe is not strongly related to its entropy.

Because of the large difference between the universe’s effective M and the maximum it could be (eg: if it really was a homogenous, ideal gas of fundamental particles), I don’t believe the 2nd Law prohibits the volume of the universe from contracting.

There are many strong arguments against the possibility of the universe contracting (eg: an closed, oscillating or “big crunch” model), most of which say something about the universe not having enough gravitational interaction to halt its expansion. I don’t believe, however, that an argument based on the 2nd Law of Thermodynamics is among them, except possibly at the point in a big crunch scenario that the universe is compressed into a very small volume. Perhaps, then, Thermodynamics argues that

• a gravitationally closed universe cannot crunch into less than a certain volume, rather like an the closed oscillations in volume of a globular cluster; or
• only a small portion of the universe – its fermion and massive bosons, perhaps – can be gravitationally closed, allowing a lot of information/disorder to escape as bosons (radiation); or
• when a contracting big crunch universe reaches a certain volume, time really does begin running backwards

I strongly doubt the last of these is possible. For all its beauty and utility, thermodynamics is really just a collection of statistical laws, describing the exceeding likely, but not the absolutely possible. If “push came to crunch”, I suspect quantum mechanical law would trump thermodynamic.

Entropy of a system should be defined as randomness of the system. However we don't know so far how many dark matters within the Universe, the chaotic molecular ramdoness is more prone to occur in the Universe. CraigD, can you explain more abt your last point?

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Anyone want to interject here with some word definitions of entropy. I believe that one must look at the system. I believe the controversy here revolves around the definitions of entropy and an expanding universe, which I believe are used in a cyclical definition. No time to look it up right now, if no one else does in the next 8 hours, I'll be back.

Before introducing a statement of the second law of thermodynamics it should be clarified the concept of reversible and irreversible processes. Generally, the state of a system and its environment are affected during a process. Two outstanding features of a process are that they may be reversible of irreversible.

A reversible process can be achieved in at least one way such that a system and its environment may be restored to their respective initial states. Conversely, a process is irreversible if it is impossible to carry out in such a way that the system and its environment can be restored to their respective initial states.

Irreversibility is a ubiquitous ‘property’ observed in most natural physical phenomenon that leads to complex, constructive formations such as vortex creation, laser light, and chemical oscillations, and from which emerges the arrow of time—from the past to present, and toward the future. Newton’s law describes a time-reversible universe, whereas the evolutionary description of nature associated with entropy is time-oriented, or time-dependent (irreversible).

Entropy is the property that determines the direction of spontaneous change.

Coldcreation

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Irreversibility is a ubiquitous ‘property’ observed in most natural physical phenomenon that leads to complex, constructive formations such as vortex creation, laser light, and chemical oscillations, and from which emerges the arrow of time—from the past to present, and toward the future. Newton’s law describes a time-reversible universe, whereas the evolutionary description of nature associated with entropy is time-oriented, or time-dependent (irreversible).

Reversiblity or irreversiblity is nothing to do with the entropy increament i suppose. I agree that the Universe is time-dependent and irreversible.

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I'm not sure, but I think you're confusing reversibility of process with reversibility of time.

I do though have a suspicion that the definition of entropy is somehow tied to the progression of time, which is what I questioned in an earlier post. Then only if the universe were to stop expanding, or time were somehow reversed could the current definition of entropy be flawed. It is a controversial subject of time reversal, and strongly believed that the universe is incapable of shrinking given it's current expansive acceleration.

Perhaps however, entropy is not tied to time or the universe, but rather is the property of the physical universe that prevents time or the expansion of the universe from reversing, thus they are tied to it.

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I'm not sure, but I think you're confusing reversibility of process with reversibility of time.

I do though have a suspicion that the definition of entropy is somehow tied to the progression of time, which is what I questioned in an earlier post. Then only if the universe were to stop expanding, or time were somehow reversed could the current definition of entropy be flawed. It is a controversial subject of time reversal, and strongly believed that the universe is incapable of shrinking given it's current expansive acceleration.

Perhaps however, entropy is not tied to time or the universe, but rather is the property of the physical universe that prevents time or the expansion of the universe from reversing, thus they are tied to it.

As i said, the Universe is Time-Dependent and irreversible. However, if the time can be reversed, irreversiblity can be reversible in space!!!

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I'm not sure, but I think you're confusing reversibility of process with reversibility of time.

I do though have a suspicion that the definition of entropy is somehow tied to the progression of time, which is what I questioned in an earlier post. Then only if the universe were to stop expanding, or time were somehow reversed could the current definition of entropy be flawed. It is a controversial subject of time reversal, and strongly believed that the universe is incapable of shrinking given it's current expansive acceleration.

Perhaps however, entropy is not tied to time or the universe, but rather is the property of the physical universe that prevents time or the expansion of the universe from reversing, thus they are tied to it.

Entropy, in its most general deffintion (applying to equilibrium and non-equilibrium processes alike) is S = k ln W (where k is boltzman's constant and W is usually written as a captial omega). Omega (W) is defined to be the number of microscopic ways to make your macroscopic state. I've always found it fascinating that a classical theory (Newton's) in which every process is reversible still leads to large scale irreversible processes.

-Will

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See, there is no dependence on time there. what about delta S, is there a time dependence there?

Or are we talking about time dependence in the case of the universe expanding and lending to a greater value for omega?

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See, there is no dependence on time there. what about delta S, is there a time dependence there?

Or are we talking about time dependence in the case of the universe expanding and lending to a greater value for omega?

The statement that entropy always increases, (or stays the same) is the statement that the system moves toward a more probable state.

-Will

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Actually I thought that there was something more to it. I thought it also said that the lowest energy state is the most stable state, which leaves out the states between that are more stable and require a catalyst to reach the next most stable state. Maybe I'm not remembering my thermo too well though.

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When entropy is at its maximum, will time still continue?

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What you need to ask first, is what will the universe be like when entropy is at a maximum?

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I think that so long as there is change, there is time. That means that even at maximum entropy there will be time.

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Actually I thought that there was something more to it. I thought it also said that the lowest energy state is the most stable state, which leaves out the states between that are more stable and require a catalyst to reach the next most stable state. Maybe I'm not remembering my thermo too well though.

The system moves to minimize what is called the free energy (different free energies for different processes). Generally processes, maximizing entropy at fixed energy, or minimize free energy at fixed entropy.

-Will

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From what I understand, according to BB cosmology, the entropy of the universe was very high to begin with, then decreased, then increased. Seems to me that that violates the second law. The same law would certainly be violated (again) if the cosmos were to shrink.

Coldcreation

Are you talking about the first few miliseconds after BB? There were fluctuations then that made it possible for matter to be more prevalent than antimatter. But seems to me the overall effect was increasing entropy since more and more matter was created from energy. To reverse entropy would mean heating things up again. (?)

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