
#1
Jul1208, 04:22 PM

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The question of the "arrow of time" and increasing entropy is not as clean cut as one might imagine. I think it it R.Penrose that pointed out that while a simple application of thermodymanis predicts the "heat death" of the universe where everything is cold and in thermal equilibrium, there is a paradox because the initial conditions of the universe just after the big bang is one of thermal equilibrium. This can be seen in the very small degree of thermal anisotropy in the CMB. THe situation for the entropy of the universe os a whole is complicatd by gravity. We know from Hawkings that the entropy of a gravitationally collapsed object (a black hole) is very high. This suggests that the expanding universe with reduction in mass energy density is an example of reducing gravitational entropy (the opposite of a black hole). So while the expansion of the universe represents increasing thermal entropy it represents reducing gravitational entropy at the same time. Many quantum cosmological models predict a "bouncing" universe that alternately collapses and expands again. That requires the total entropy of the universe to be constant over time as only constant entropy processes are reversible. That suggests that maybe thermal and gravitational entropy work in opposite directions and cancel each other out. It would be kinda cool it the total energy of the universe is always zero, the total charge of the universe is zero, the total linear and angular momentum is zero and the total entropy of the universe is always zero.




#2
Jul1208, 05:35 PM

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#3
Jul1208, 05:53 PM

Mentor
P: 6,040

Penrose says exactly the opposite. The universe clumps as it expands. According to Penrose, this gravitational clumping causes an increase in entropy that dominates changes in entropy due to other processes. Why is there a second law of thermodynamics? I don't know if there is agreement on this, but some physicists, including Roger Penrose and Sean Carroll, think that the second law has a cosmological origin. In the blog entry http://cosmicvariance.com/2007/06/11...arrowoftime/ Sean Carroll concludes 



#4
Jul1208, 07:29 PM

P: 3,967

Entopy and Cosmology
Hi George and JesseM,
Anyway, here are some simple observations: Take an insulated partitioned box with hot gas on one side and cold gas on the other side. Remove the partition and the gas molecules mix going to state of thermal equilibrium. (E1) A universe with an initial condition of thermal equilibrium = High Entropy. Take a gas cloud that has gravitationally collapsed to a high density black hole. Hawkings black hole entropy equations show that a state of gravitational collapse is a state of maximum entropy. (E2) A universe with high initial density = High Entropy. Take a cloud of gas with a high initial temperature in a small volume that is not gravitationally bound and it will expand, increasing the volume and degrees of freedom and cooling at the same time. So high temperature and low volume is a state of low entropy. (E3) A universe with high initial temperature and low volume = Low Entropy. So in calculating the initial entropy of the universe we should not take any one of the forms of entropy described above (and there are probably others) in isolation, but rather consider and combine all forms of entropy to give a total entropy of the form TE = E1+E2E3 with the possibility that TE is an invariant quantity possibly equal to zero as far as the universe is concerned. Jambaugh in the Quantum Physics forum of PF gives an interesting Quantum Mechanical argument for the entropy of the universe being zero here: http://www.physicsforums.com/showthread.php?t=170493 



#5
Jul1208, 08:14 PM

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By the way, the audio wasn't working for me on that pageif anyone else has this problem, I found an mp3 of the audio here, you can start it a few seconds after the video starts and it'll be approximately synched up. 



#6
Jul1208, 08:14 PM

P: 3,967

One form of entropy I have not really discussed is structural or information entropy. A poplular notion of increasing entropy is increased randomness or chaos with structure representing a low state of entropy. I am not sure how this fits into the overall picture. However a definite pattern emerges from the thress form of entropy I have described above and that is that increasing entropy of any one type represents a loss of potential energy and the ability to do work. A high temperature gas in a small volume has high pressure and an obvious capacity to do work and the arrow of time moves in the direction of reducing that potential energy so that you end up with a low temperature, low pressure gas in a large volume that has less potential to do work. A gravitationally bound cloud of gas has high gravitational potential energy and the arrow of time dictates that it moves to a lower graviational potential. When the gas cloud collapses it heats the gas and increases the pressure possibly forming a star. The loss of gravitational potential energy and increase in gravitational entropy has resulted in an increase of thermal potential energy and a reduction of thermal entropy. This hints at the interchangeabilty of forms of entropy working dynamically together. A box of hot gas and cold gas going to thermal equilibrium represents a loss of potential energy as the thermal gradient that was available to do work has been lost.
Here is a simple thermodynamic thought experiment. A cylinder is filled with gas and the gas is retained by an internal spring attached to a piston. Outside the cylinder is a vacuum and the cylinder is perfectly thermally insulated. The spring pulling the piston inwards puts the gas under pressure. The system could stay static with the force of the spring exactly equal to the force of the gas acting on the piston. Now if the piston is sharpely tapped to give it inward momentum the pressure and temperature of the gas increasesand this is enough to halt the piston and start it moving outwards. As the piston moves outwards the retaining spring's potential enrgy increases and eventually it stops the piston and sends it back into the cylinder increasing the pressure and starting the cycle again. If the piston was perfectly frictionless and if the cylinder was perfectly insulated this oscillation would continue forever as the thermal potential energy is converted into the potential energy of the stretched spring and vice versa. The total entropy of the system remains constant as an increase in thermal entropy is compensated by the reduction of entropy in the stretched spring. Now a real spring and cylinder could not be perfectly frictionless and perfectly thermally insulated, BUT the universe as a whole can. 



#7
Jul1208, 09:13 PM

P: 3,967

 (E1) A universe with an initial condition of thermal equilibrium = High Entropy. (E2) A universe with high initial density = High Entropy. (E3) A universe with high initial temperature and low volume = Low Entropy. (E4) A universe with initial smooth gravitational geometry (low clumpiness) = Low entropy. So in calculating the initial entropy of the universe we should not take any one of the forms of entropy described above (and there are probably others) in isolation, but rather consider and combine all forms of entropy to give a total entropy of a form something like TE = (E1/E3)(E3/E4) with the possibility that TE is an invariant quantity possibly equal to zero as far as the universe is concerned.  It is interesting to note the dynamic changes in entropy as the universe evolves. In the initial universe: Thermal equilibrium (High entropy) Smooth geometry (Low entropy) High temperature (Low entropy) High gravitational density (High entropy) As the early universe progressed structures such as galaxies formed increasing entropy due to increased clumpiness, the overall temperature cooled increasing entropy, stars formed local hot spots providing thermal gradients reducing entropy and the universe expanded increasing entropy because of increased volume and reducing entropy because of the increasing gravitational potential. Early universe: Thermal gradient as stars form (Low entropy) Gravitaional gradient as structures form (Increasing entropy) Falling temperature (Increasing entropy) Reducing mass density (Reducing entropy) Current universe: Tendancy towards thermal equilibrium as stars burn up (Increasing entropy) Increased gravitational gradient as more mass ends up in black holes (Increasing entropy) Falling temperature (Increasing entropy) Reducing mass density (Reducing entropy) Late universe: Thermal equilibrium (High entropy) All matter in black holes (High entropy) Low temperature (High entropy) Reducing mass density (Reducing entropy) Very late universe: Thermal gradient as black holes evaporate (Reducing entropy) Smooth geometry as the black holes evaporate (Reducing entropy) Low temperature (High entropy) Reducing mass density (Reducing entropy) Final universe? Thermal equilibrium (High entropy) Smooth geometry  no black holes (Very Low entropy) Low temperature (High entropy) Reducing mass density (Reducing entropy) I have assumed a universe that contimues to expand forever. If it was to collapse then: Collapsing universe: Thermal equilibrium (High entropy) Smooth geometry  no black holes (Very Low entropy) Increasing temperature (Reducing entropy) Increasing mass energy density (Increasing entropy) Those are of course VERY rough back of envelope estimates of entropy and other forms of entropy such as chemical/structural/chaotic/information entropy might have to factored in. As I mentioned before, it is an interesting possibilty worth investigating, that the total entropy of the universe in all it forms is invariant, opening up the possibilty of dynamic cyclic eternal models rather than a universe on a one way thermodynamic trip to an inevitable "heat death". As I mentioned before, the cyclic models that keep turning up in quantum gravity models with alternating expansions and cruches require total entropy to be invariant. 



#8
Jul1208, 11:08 PM

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#9
Jul1308, 09:48 AM

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#10
Jul1308, 09:49 AM

P: 143

I think it should be interpreted as follows. The universe starts out in a maximal entropy state, indeed, despite that it was totally unordered, but for reasons of the geometry. Now entropy runs down in the universe as one normally would expect. But he then theoretizes what would happen with the universe in the long run, accelerated expansion and hawking radiotion would eventually tear apart all normal matter, and supposedly lead to a universe with only radiation. He then states that the universe more or less forgets about time (if there is no matter, there is no way of measuring time anyway), and you can rescale the universe and then *magically* return to the original configuration of the universe in a maximal entropy state. If there is infinity entropy anyway, entropy can run down eternally without problem. 



#11
Jul1308, 10:02 AM

P: 3,967

One idea in relation to Penrose's idea is this. If the universe eventualy reaches a state of being radiation dominated after all the black holes have evaporated, then if the universe was initially finely balanced between expansion and collapse when it was matter dominated it would be tilted in the direction of collapse when it is radiation dominated. This is because the gravitational influence of all the energy of the universe in the form of radiation is greater than than when the energy is the form of mass. At least that is the impression I get from the curvature of the radiation dominated universe being proportional to (t/t0)^(1/2) and the curvature of the mass dominated universe being proportional to (t/t0)^(2/3) for a mass dominated universe. 



#12
Jul1308, 12:38 PM

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