Re: Entropy

From: David_Bowman@georgetowncollege.edu
Date: Mon Oct 23 2000 - 23:15:44 EDT

  • Next message: Stephen E. Jones: "Houston Chronicle on Demski's removal"

    Regarding Richard Wein's question:

    >Dave, thanks for all the info about 2LT. To be honest the details are beyond
    >me. As a non-physicist, it would be nice to have a simple way of rebutting
    >the creationist/ID argument, if there is one.

    Which "creationist/ID argument" do you mean? The general argument that
    ID is detectable in nature, or the specific argument that the 2nd law
    opposes natural self-organization of material systems? Or something else?
    If you mean the argument that the 2nd law prevents spontaneous-self
    organization, I suppose the simplest rebuttal is to point out that the
    2nd law doesn't address the issue of the macroscopic organization of
    matter or its lack one way or the other, and that some processes in
    nature self-organize and some self-disorganize, and some have complicated
    mixtures of both, that all these cases are fully consistent with the
    operation of the 2nd law, and that for none of these cases is the 2nd
    law "overcome", "circumvented", made inapplicable, etc.

    >It seems to me sufficient to point out that the 2LT only applies to closed
    >systems and that living organisms are not closed systems. Is this a fully
    >adequate argument?

    Not really. The 2nd law applies to all systems of a macroscopic number
    of microscopic degrees of freedom, whether or not the system is closed.
    It's just that when the system is closed the formulation of the law is
    simpler and cleaner. When the system is closed the 2nd law states that
    the thermodynamic entropy of the system is nondecreasing in time. When
    the system is coupled to its environment so it is not closed off from its
    surroundings (w.r.t. energy-exchanging interactions among the degrees of
    freedom of the system and those of the environment) then the system's
    entropy alone is insufficient as a relevant parameter for the 2nd law.
    For such an open system the system's entropy may go up or down, or
    oscillate in a host of complicated ways with time. *But* whatever it
    does, the *sum* of the system's entropy *and* the contribution to the
    entropy of the system's surroundings pertaining to the environmental
    degrees of freedom that happen to interact with the system and with each
    other *does* increase (or at least doesn't decrease) with time. The
    minimal part of the environment's entropy that needs to be included in
    this sum is the entropy that is generated in the environment by virtue of
    the interaction of of the degrees of freedom of the environment with the
    system and with each other. Because we can always surround any system
    with a bigger environment we are safe to say that the total entropy of
    the universe always increases with time. This last formulation
    effectively takes the whole universe as the system so there are no
    surroundings to worry about.

    Since it is a royal pain to have to deal with the goings on of both the
    system at hand and its environment (which could conceivably be the whole
    rest of the universe) it is very desirable to have a formulation of the
    2nd law that only makes reference to what is going on in the system and
    not in the environment. Such a formulation is possible in some
    circumstances such as when the environment plays a relatively innocuous
    background role that merely enforces some macroscopic constraints on the
    system.

    For instance, suppose the system's immediate environment is maintained
    at a constant temperature and acts as a heat reservoir for the open
    system (where heat is allowed to be freely exchanged between the system
    and its surroundings). Then in this case the 2nd law is modified to
    *not* refer to the system's entropy, but to its so-called availability or
    free energy. In this case the system's free energy *decreases* (or at
    least doesn't increase) with time. (As the system's free energy is
    monotonically decreasing, its entropy may be increasing, decreasing, or
    oscillating). The system's equilibrium state occurs when the system is
    equilibrated with itself and its environment and has the environment's
    temperature throughout. When the system is in equilibrium then its free
    energy is *minimized*.

    Now there are multiple definitions of free energy because which kind of
    free energy is the relevant one for a given situation depends on some of
    the other constraints of interaction that exist between the system and
    its environment. For instance, if the environment of the system forces
    the system to have a fixed constant volume and the system is effectively
    a fluidic system then the pressure exerted on the system by the
    environment is subject to change as time goes on, and the relevant free
    energy is the Hemholtz free energy.

    But if, instead, the environment maintains a constant pressure and
    temperature on the system, then a fluidic system's volume is allowed to
    change with time. In this latter case the relevant free energy that
    decreases is the Gibbs free energy. If the boundary between the system
    is permeable to particle fluxes, then the relevant free energy is
    something else. If the system is an anisotropic solid, then the relevant
    free energy is, again, something else. Etc., etc.

    >I seem to remember some creationist claiming that there's a form of the 2LT
    >that applies to open systems. Is that true?

    Yes. See above.

    >Or perhaps he was talking about informational entropy, which has nothing
    >to do with the 2LT. Any comment?

    Actually, as I explained in my previous long post, the thermodynamic
    entropy is a *special case* of "informational entropy". All kinds of
    entropy are "informational" in the sense that they all measure the
    average amount of *information* missing in a context of uncertainty
    where, because of the uncertainty, there are multiple possible outcomes
    consistent with what is known about the situation, and a probability
    measure can be defined on the set of those outcomes. The entropy is a
    functional on the probability distribution. Each probability
    distribution has its own (information theoretic) entropy. It just so
    happens that the thermodynamic entropy of a physical system is the
    "informational entropy" associated with the probability distribution of
    the system's microscopic states consistent with the macroscopic
    description of that system. But it is *only* the thermodynamic entropy
    that is subject to the 2nd law of thermodynamics. The other kinds of
    entropy are not required to increase with time for an isolated system.
    In general, the other kinds of entropy don't have to obey any particular
    special laws other than that the entropy be a nonnegative real number
    for any given discrete probability distribution. Also various
    conditional entropies would typically have to satisfy a few sum rules as
    well so as to keep all the different conditional entropy measures
    mutually self-consistent. BTW, there are other kinds of entropy that
    can have physical significance for a physical system besides the
    thermodynamic entropy. But any non-thermodyamic entropy doesn't
    necessarily have any particular trend with time.

    >Thanks for your help.
    >
    >Richard Wein (Tich)

    I'm not sure I've been any help, but you are welcome to it, such as it
    is.

    David Bowman
    David_Bowman@georgetowncollege.edu



    This archive was generated by hypermail 2b29 : Mon Oct 23 2000 - 23:20:35 EDT