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What's the boundary between micro and macro?

  1. Aug 17, 2004 #1
    Thermodynamics treats with macroscopic systems, where statistical mechanics make sense. In these systems there is an arrow of time following the second law. On the contrary, temporal reversibility is generally seen at microscopic level.

    What is the limit (magnitude order in number of molecules or other) where a physic system must be seen from a thermodynamic viewpoint?

    One isolated live cell would be a thermodynamic system: it ages. That also occurs in subcellular systems as mitochondria. But, what's about a discrete sample of cell macromolecules? Make it sense to talk on thermic differences inside a live cell?

    ¿When a microscopic system should be named macroscopic and to be object of thermodynamics?
  2. jcsd
  3. Aug 17, 2004 #2


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    Hey, another spanish over here!. :tongue2: The moment in which official language of this forum will be the spanish is nearby....

    Your question is very interesting. Thermodynamics employs some results of the kinetic theory. To be honest, I don't know what is the amount of molecules neccesary in the limit between Thermodynamic and Kinetic Theory. But you should know when we employ thermodynamics equations (like first principle), we are assuming the next hypothesis implicitly:

    The continuous medium: inside a thermodynamic system there have to be a minimum amount of molecules. How many?. The neccesary such density function (rho(x,y,z,t)) is continuous and derivable in space and time. This critical amount is reached when thermodynamics variables changes smoothly enough to be yielded in thermodynamics differential equations. This threshold is reached when the infinitesimal volume analyzed has a characteristic lenght larger than the free characteristic running (recorrido libre característico).

    When smaller scales are analyzed, thermodynamics equations are not valid at all, in part because their differential operators have no sense.

    Are you waiting for a global theory?. Well, sit down and wait, wait long... :zzz:
  4. Aug 18, 2004 #3
    I believe the difference occurs when the wavelength of the object is large enough in the system not to be ignored, each object with mass has a particular wavelength
    electrons have wavelengths of the order of the atom hence quantum mechanics , but protons having 1000 x mass , have far smaller wavelengths hence nuclear physics .
    The mass of a cell by comparison is huge and it's wavelength extremely small so as a whole it behaves as a macro object.
  5. Aug 18, 2004 #4
  6. Aug 18, 2004 #5


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  7. Aug 19, 2004 #6
    In a simplistic view, a cell is a colloidal solution isolated by a lipidic membrane. Inside the cell there are also membranes isolating subcellular structures:
    Please see the figures of http://www.emc.maricopa.edu/faculty/farabee/BIOBK/BioBookCELL2.html#The%20Cell%20Membrane [Broken]
    Quantitatively, the most abundant intracellular molecule is water.
    Membranes are constituted by a fluid phospholipid bilayer where "float" proteins with more or less freedom. In this structure, two types of molecules are important: phospholipids (hydrophobic interaction) and proteins (freedom to move into the bilayer
    Last edited by a moderator: May 1, 2017
  8. Aug 25, 2004 #7
    Of course, a live cell is a very complex system.
    I have seen some works (very few) where a mesoscopic approach was used to study lipid bilayers (the basic structure of a biological membrane).
    This is an example: http://www.biophysj.org/cgi/reprint/83/6/3357.pdf [Broken]

    In a simple system, such a as a collection of hydrogen molecules, what would be the magnitude order of particle number to pass from a classical mechanics view to a statistical mechanics approach?
    Last edited by a moderator: May 1, 2017
  9. Aug 26, 2004 #8


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    I have not any idea about Biology, but I'm going to explain you how is it done with an ideal gas.

    Inside an arbitrary volume, there will be certain number of molecules according to the gas density. Then, obtain the average volume filled by only one molecule. The main free path [tex]\lambda[/tex] is the cubic root of this volume.

    For [tex]d<<\lambda[/tex] it will be impossible to employ classical thermodynamics due to severe changes in density [tex]\rho[/tex].

    Best regards.
  10. Aug 26, 2004 #9


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    Ah! and damn USA basketball team! They have kicked us off out of Olimpic Games!

    Brrrr...... :mad: :mad: :cry:
  11. Aug 26, 2004 #10
    Thank you for your answer Clausius2.
  12. Aug 26, 2004 #11
    Los españoles somos la leche, en cuanto nos vemos por el mundo adelante nos dedicamos a armarla buena jeje ...

    Digo yo, si a este mensaje sólo respondemos españoles, para qué hablar en inglés ?

    Creo que la termodinámica establece la frontera en donde la cuántica empieza a fastidiar un poco.

  13. Aug 26, 2004 #12
    Ya, pero lo lee más gente de la que contesta. :rolleyes:

    Of course, there is a boundary between the classical mechanics description and the thermoynamic view. I think that for a simple collection of particles, the answer of Clausius2 is enough clear.

    Saludos. Me alegro de que haya presencia española en este foro. :smile:
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