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Phase Space

  1. Dec 9, 2004 #1
    I just read Penrose's explanation of entropy in his book "The
    Emperor's New Mind". His explanation is completely saturated in an
    extended discussion of "phase space" . Is this concept of "phase
    space" absolutely necessary in order to explain or understand
    entropy ?

    Celal
     
  2. jcsd
  3. Dec 9, 2004 #2

    Tide

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    The short answer to your questions is "No, it it not absolutely necessary!"

    I haven't read Penrose's "The Emperor's New Mind" so I don't know exactly what he's doing and why. However, I am looking forward to his new book "The Road to Reality : A Complete Guide to the Laws of the Universe" due out in February.
     
    Last edited: Dec 9, 2004
  4. Dec 9, 2004 #3

    dextercioby

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    Depends on how rigurous u want to be.The concept of entropy really belongs to statistical physics,and not to thermodynamics.As each theory is presented 2 distinct (logically equivalent) formulations,i guess it all depends on how rigurous u wanna be.If u're one Penrose kind (and i'd like to think of myself being so (theory inclined)),u couldn't conceive the notion of entropy without abstract separable Hilbert spaces and the phase space.

    Daniel,

    reccomending u read "Emperor's new mind".

    EDIT:Sorry for the repetition.I could have found other words,not the same.
     
  5. Dec 9, 2004 #4

    Clausius2

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    I'm not sure about that. What was the first? Thermodynamics or Statiscal Mechanics? When Clausius formulated the second principle the Entropy function was well defined yet, and it had completeness and a meaning, wasn't it?

    I'm confused about that, I'm not stating what I've posted at all. Anybody could clear it up?
     
  6. Dec 9, 2004 #5

    dextercioby

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    My friend,history of science is one thing,logical relations among theories in science are another.
    There would not have been statistical thermodynamics (thermodynamics of statistical systems) without prior knowledge and notions/concepts form thermodynamics.That's history.Yet,thermodynamics as a whole is a subtheory of statistical mechanics.Every principle of thermodynamics can be thoroughly derived from the laws of classical/quantum SM.That's science.

    Proof of my statements can be given if one is considering SM in the microcanonical ensemble and classical thermodynamics of reversible phenomena in the Neogibbsian formulation.
    Your postulate of Clausius can be proved via Boltzmann equation.

    Daniel.

    PS.I loved your exposure on "swirling water while draining".YOU'RE A MASTER.
     
  7. Dec 10, 2004 #6

    Clausius2

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    :blushing: :blushing: Thanks Daniel, I love you too :!!) :rofl: :cool: .

    Well, to say the truth I have NO idea about phase space. In fact I only know a bit about Kinetic Theory. Maybe I didn't go to class that day.... :biggrin: . I have nothing to say, you know more about this.
     
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