XPost: sci.astro.research   
   From: roland.franzius@uos.de   
      
   Am 02.06.2017 um 12:07 schrieb Phillip Helbig (undress to reply):   
   > In article ,   
   > Gerry Quinn  writes:   
   >   
   >>>> To put it another way, the 'clumpy' states in the non-gravitational   
   >>>> universe have lower entropy than the smooth state, but the clumpy states   
   >>>> in the gravitational universe have higher entropy than the smooth state.   
   >>>   
   >>> Imagine a clumpy universe with no gravity.  It has low entropy (lower   
   >>> than the smooth universe).  Now G starts increasing from zero to, say,   
   >>> its current value (at which point the clumpy universe has a higher   
   >>> entropy than the smooth universe).  At some value of G, the clumpy   
   >>> universe must have the same entropy as the smooth universe (which you   
   >>> say has the same entropy with or without gravity).  So for this value of   
   >>> G, the entropy is independent of the clumpiness.   
   >>>   
   >>> Someone has made an error somewhere.   
   >>   
   >> Why should it not be independent of the clumpiness?   
   >   
   > Because it's not.  A room full of air with the same density everywhere   
   > has higher entropy than a room with all of the air squeezed into one   
   > corner.  (In the case where gravity can be neglected.  When gravity   
   > plays a role, then the clumpier distribution has higher entropy.)   
   >   
      
   This kind of comparison needs a gas, a process that is adiabatic for one   
   leg and isothermal for the other leg of a reversible path in state spece   
   and therefor at least one thermal bath.   
      
   Because all such things do not exist in the universe of lets say a gas   
   of galaxies or photons or hydrongen and helium all kinds of modelling of   
   entropy along the classical examples of gas in a variable volume and and   
   two temperatur baths at hand are highly doubted in the community.   
      
   Finally, the two volumes of a system at two times are the 3d-boundaries   
   of a 4-volume, bottom and ceiling orthogonal to the direction of time.   
      
   With a nonstationary 3-geometry in the rest system volume changing has   
   no thermodynamic effect because all particles and fields follow their   
   unitary or canonically free time evolution in a given Riemann space.   
   That does not change the von Neumann entropy because of Liouvilles   
   theorem of constancy of any 6-volume element of spce and momentum.   
      
   Finally for interacting system of fermionic particles and fields at   
   temperatures below the Fermi temperature, a state with lumpy matter and   
   a small fraction of free gas over its surface is the state of maximal   
   entropy.   
      
   Interacting matter evenly distibuted in a given volume that it does not   
   fully occupiy as a condensed body is highly improbable.   
      
   --   
      
   Roland Franzius   
      
   --- SoupGate-Win32 v1.05   
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