Hi David;
thanks for responding
The way I see it .....
David Bowman wrote:
>
> We certainly don't need to look at anything as exotic as a
> "maintained far--from--equilibrium" system to see a decrease in
> entropy. All we have to do is observe *any* system placed in thermal
> contact with some other object which is at a somewhat lower
> temperature than the system of interest. When the hotter object
> cools by heating the cooler object the hotter object's entropy
> decreases. This can and does happen even for systems that are
> infinitesimally away from equilibrium.
Evidently, we agree on the main point that it is necessary to define one's
system when speaking about entropy since you too allow for an entropy
decrease at the cost of the surroundings; however, you confine yourself to
equilibrium thermodynamics. Contrarily, far--from--equil. systems are not
exotic at all. They are very common and quite literally define the regime
in which "the action is" when discussing large scale evolution; i.e., not
fluctuations about equilibrium.
Respectfully, it is my opinion, that the notion of infinitesimals is in
fact very exotic in that they are mathematical constructions created to
avoid actual infinities. They arise in thermal dynamics when discussing
the idealization of reversibility; i.e. they are introduced to allow a
system's temperature, T, to change slow enough to allow reversibility so as
to apply dQ/T, T=constant (or change a system's T without changing
T!)--but, as you attest to later, natural systems undergoing evolution are
manifestly irreversible and therefore equililbrium thermodynamics doesn't
apply since they are seen to be far-from-equil.
Calculus later introduced infinitesimals to save us from going mad
contemplating infinities :-) .
> The entropy of the Sun is *decreasing* (maybe Andrew just mistyped
> his comment here)--recall the temperature of the Sun is higher than
> that of interstellar space.
Thank you, I did mean decreasing; (BTW, if you were referring to me, I am
George.)
> Also, the claim "entropy LOCAL decreases as evolution progresses"
> is ill-defined, and as such, may or may not be true in some
> circumstance depending on just *which* entropy is being considered.
But entropy to which YEC refer is that which is defined by the second law;
i.e., in terms of energy (thermal) or logarithmic functions of accessible
phase--space state densities (Stat. Mech.). (There really are no others;
just analogies to this one; e.g. information entropy.) As such, it is
applicable to biological systems; a fact you attest to when referring to
irreversibility and dissipation in the following statement:
> But overall, biological processes (including those that result in
> evolution) are irreversably dissipative, and as such they generate
> net entropy.
True, energy input from the surroundings (eat, drink and get some Sun :-) )
is required for (most) biological systems to maintain their far--from-
equil. state.
Thanks.
George.
-- George A. Andrews Jr. Physics/Applied Science College of William & Mary P.O. Box 8795 Williamsburg, VA 23187-8795
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