Entropy and derivations - is my logic faulty?

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Discussion Overview

The discussion revolves around the concept of entropy in the universe, particularly in relation to the derivation of fluid and acceleration equations in cosmology. Participants explore the implications of assuming that entropy increases, while also examining the conditions under which certain equations are derived, including the role of adiabatic processes and temperature considerations.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that if dQ is set to zero in the derivation of fluid and acceleration equations, then dS should also be zero, suggesting a conflict with the assumption that entropy increases.
  • Others argue that the universe's expansion is adiabatic, meaning there is no heat transfer, which supports the idea that dQ equals zero.
  • Some participants question the relationship between temperature and energy density in a homogeneous universe, noting that the temperature of the cosmic microwave background (CMB) is not necessarily representative of other components in the universe.
  • There are requests for references to support claims about the derivation of equations and assumptions made in textbooks, with some participants providing specific sources while others express confusion about the relevance of these references.
  • Several participants highlight that certain sources explicitly assume that entropy does not increase, raising questions about the validity of the initial assumption that entropy increases in the universe.
  • Participants discuss the continuity and acceleration equations, with some clarifying their definitions and how they relate to the Friedmann equations.

Areas of Agreement / Disagreement

Participants do not reach consensus on the relationship between entropy, temperature, and the derivation of cosmological equations. Multiple competing views remain, particularly regarding the assumptions made in various sources and the implications of adiabatic processes.

Contextual Notes

Some participants express uncertainty about the definitions and implications of terms like "continuity equation" and "acceleration equation," indicating a potential lack of clarity in the discussion. There are also references to specific sections in textbooks that may not align with the claims made by other participants.

  • #31
For an isolated system like the universe, the Clausius inequality reduces to $$\Delta S\gt\int{\frac{dq}{T}}=0$$This means that, even with no heat transfer to the system (dq=0), entropy is generated with the system itself, and thereby increases.
 
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  • #32
Nick Prince said:
The entropy of sub systems is additive

There are no "subsystems" in the Friedmann models, or in the thermodynamics based on them that you referenced. There is just one homogeneous, isotropic universe.

Nick Prince said:
so the overall entropy of the universe must be greater than zero

For our actual universe, yes, I agree. For the idealized universe in the Friedmann models, however, you might want to rethink this statement.

Nick Prince said:
This must be equal to T dS

No, ##T dS## is the change in entropy as a result of some process. If the process is adiabatic, as the expansion of the homogeneous, isotropic universe is in the Friedmann models, then ##dS = 0##. Your references make that clear. What they do not discuss at all is what other processes might be taking place in the actual universe (as opposed to the idealized universe in the Friedmann models) that might increase entropy.
 
  • #33
PeterDonis said:
No. But that does not mean I think entropy is increasing in the idealized models of a homogeneous, isotropic universe based on the Friedmann equations. Your references make it obvious that it is not. So, if entropy is in fact increasing in our universe, it is obviously doing so as a result of some process that is not included in those idealized models.
So the implicit starting assumptions are wrong and hence the friedmann's accn and continuity equation are not complete?
 
  • #34
Nick Prince said:
So the implicit starting assumptions are wrong and hence the friedmann's accn and continuity equation are not complete?

Do you think the equations in the references you gave are complete models of everything that happens in the universe?
 
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  • #35
PeterDonis said:
Looks ok, I was able to get to the URL and see the quote you gave.
Yes, but this still doesn't say how energy density is related to temperature.
This T is the T of the CMB. It's not the same as the T of other components of the universe. The link you gave discusses two kinds of components: radiation (of which the CMB is an example) and cold non-relativistic matter. What is the T of the latter?
Thats nice then

Well I mean to radiation energy density. And radiation energy density has a relationship with tempature.

I mean the CMB.
 

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