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Entropy of the Universe 
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#19
Dec812, 09:51 AM

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An isolated system is one in which nothing, neither energy (whether in the form of heat or work or whatever) nor matter (mass) crosses the boundary. A closed system is one in which energy (work ,heat etc) may be transferred across the boundary but matter (mass) may not. So, of necessity an isolated system is also a closed one. 


#20
Dec812, 01:27 PM

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#21
Dec812, 06:56 PM

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This seems to be the case with the Universe; what macroscopic variables would you choose to describe its state? 


#22
Dec812, 09:29 PM

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#23
Dec912, 10:07 AM

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#24
Dec912, 11:15 AM

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The universe started in a high density, high temperature and low entropy state. The universe in this state is commonly referred to as the Big Bang. As time goes on, it is asymptotically approaching a zero density, zero temperature and high entropy state. This asymptotic limit is often referred to as the Heat Death. Entropy is a well defined quantity even in a non equilibrium state. However, it is defined in terms of a hypothetical series of reversible transitions. The Zeno "paradox" seems to have resurfaced yet again. The OP has given an argument that entropy can't be increasing because any irreversible process can be broken up into a series of reversible processes. The argument is formally similar to the argument that nothing can move because each motion can be broken up into a series of not moving steps. This argument against motion was used by the classical Greek philosopher, Zeno. He was trying to prove that logic isn't sufficient in analyzing the real world. The thermodynamics argument formally maps onto Zeno's paradox because on a subatomic level, all irreversible processes occur due to the motion of particles. Lots of work has been done on resolving "Zeno's" paradox. Whether you except these "resolution arguments" is up to you. However, I will rephrase Zeno's paradox in terms of thermodynamics. Any irreversible process lasting a finite amount of time can be broken down into an infinite series of reversible processes each lasting an infinitesimal amount of time. "Infinitesmal time" means "in the limit of zero time". Since each step is reversible, there should be no such thing as an irreversible process. "Irreversible processes occur" despite this argument. Therefore, one can claim that logic doesn't work in thermodynamics. However, I present two argument against this conclusion. "Infinitesimal time" is not the same as "zero time". An "infinitesmal time" is a hypothetically "the limit" as the time approaches zero. The mathematical meaning of "limit" has been analyzed extensively since the time of Zeno. "Limits" are mathematical and logically defined and analyzed. "Being "the limit" is not mathematically the same as "being equal to". So an infinite series of "infinitesimal processes" can add up to a "finite process" using strict mathematical formalism. Another argument for logic is that energy and momentum is quantized according to quantum mechanics. Therefore, there really is no such thing as an "infinitesimal reversible process". Both arguments are antiintuitive to many people. The last is really a cheat since no self consistent quantum mechanical theory has been found consistent with astronomical observations. However, I am done if you agree that the problem is a modified version of Zeno's paradox. I think an in depth discussion of Zeno's paradox would within forum guidelines as long as it took place in the mathematics part of the forum. There are a whole bunch of scientific problems that can be mapped onto Zeno's paradox. Some people reject biological evolution on the basis of Zeno's paradox. We see here that someone has a problem with thermodynamics due to Zeno's paradox. Since practically every branch of science uses the mathematical concept of "limit", Zeno's paradox can turn up anywhere. So the problem is the concept of limit, not with thermodynamics. 


#25
Dec912, 04:39 PM

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There are several Zeno paradoxes.
The resolution of the one about the semidistance relies on the limit [tex]\mathop {\lim }\limits_{n \to \infty } \frac{1}{{2n}} = 0[/tex] Which leads to the sum [tex]\sum\limits_1^\infty {\frac{1}{{2n}}} = 1[/tex] What particular limit are you referring to? 


#26
Dec912, 05:52 PM

P: 741

I am not sure what the corresponding mathematical expressions are. In any case, obviously entropy is increasing in the universe. The universe is "quasistatic" only over very small time intervals. It is not static. The sum of a large number of short interval irreversible processes is an irreversible process. A short 


#27
Dec912, 07:18 PM

PF Gold
P: 1,165

If we want to talk about entropy of Universe, we have to define it first, and the standard sdefinition [itex]\Delta S(1~to~2) = \int_1^2 \frac{dQ}{T}[/itex] does not apply for the Universe; there is no 1 or 2 and there is no [itex]T[/itex]. 


#28
Dec912, 07:54 PM

P: 5,462

Hello Jano, why can Darwin not use the other standard definition of entropy?
S(E,V,N,α) = k lnΩ(E,V,N,α) 


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