Re: Lizard engines and rat engines


"Tim Tyler" <tim@xxxxxxxxxxx> wrote in message news:db2792$2a42$1@xxxxxxxxxxxxxxxxxxxxxx
> Guy Hoelzer <hoelzer@xxxxxxx> wrote or quoted:
>
> > Rather than having a second law that merely limits the scope of potential
> > outcome of a dynamic process to those that do not decrease the entropy of a
> > closed system (IMHO this is code for the universe as a whole), many
> > physicists are coming to appreciate a law that favors the emergence of
> > systems that increase the RATE of entropy gain in closed systems through
> > self-organization.
>
> Dissipative structures *do* emerge. Presumably they do so because they
> are thermodynamically favoured. And they certainly do "dissipate" -
> i.e. increase the local rate of entropy gain.
>
> IMO, the first thing that needs to be done it to characterise the
> thermodynmic behaviour of self-organising systems in more detail.
> Obviously, they increase the rate of entropy increase ...

Not obvious to me. In fact, counterintuitive. I think you are being
misled by the obvious fact that dissipative structures tend to arise in
situations where entropy production is high. But I don't see how it
can be said that they are the *cause* of the entropy production.

Consider a Benard cell setup, with two copper plates and water in between.
Pump heat into the bottom plate, and extract heat from the upper plate.

When a small amount of heat is flowing, conduction transfers heat from
the lower plate to the upper. The entropy of the universe is increasing,
of course. But the rate of entropy increase has absolutely nothing to
do with what is happening between the two plates. It is a function of
the heat flow, the temperatures of the plates, and the heat capacities
of the **surroundings** of the two plates.

Let us look at the process of heat conduction through the liquid in more
detail. Plot temperature of the liquid vs distance from the lower plate.
Clearly we will have a smooth curve. But what curve, exactly. Prigogine
proved a theorem dealing with this question that won him a Nobel. The
curve will be the one that MINIMIZES the energy production within the
liquid.

Ok. Now let us increase the amount of heat flow so that conduction can
no longer handle the load. We now have convection. Benard cells form.
Dissipative structures. Self-organization. The entropy of the universe
is now increasing faster than it was in the case of conduction. OF COURSE
entropy is increasing faster. More heat is flowing. But, assuming the
convective system is in a steady state, it is still the case that the
rate of entropy increase has absolutely nothing to do with what is happening
between the two plates. It is a function of the heat flow, the temperatures
of the plates, and the heat capacities of the surroundings of the two plates.

Is there an analogy to Prigogine's theorem of minimal entropy production
for this case? Prigogine and the Brussels school sought such a theorem,
but so far they haven't found one. The problem is how to define entropy
production in a case like this. Or perhaps the problem is determining
what concept should replace entropy production. However, it is clear
that the entropy production *by conduction* is LOWER in the convective
case than in a hypothetical conductive case at the same temperatures and
heat flow.

Increase the heat flow even more. Now the liquid begins to boil, rather
than convecting. Heat flow now occurs as water evaporates at the lower
plate, bubbles upward, and then condenses at the upper plate. This process
is not AFAIK considered to be a dissipative structure (even though dissipation
is taking place). The entropy of the universe is now increasing even faster
than it was in the case of convection. OF COURSE entropy is increasing
faster. More heat is flowing. But, assuming the boiling/condensing system
is in a steady state, it is still the case that the rate of entropy increase
has absolutely nothing to do with what is happening between the two plates.
It is a function of the heat flow, the temperatures of the plates, and the
heat capacities of the surroundings of the two plates.

So, if someone wants to say that the convective system increased the rate
of entropy increase in the universe, what is it that they are saying?
Increased compared to what? Should we compare a system that exhibits
convection with one in which convection is stymied (perhaps by a system
of baffles)? It is not at all clear to me what the conjecture is that
Tim considers "obvious". I will note this: If you put in the baffles,
the system will switch to boiling/condensing at a lower heat flow than
it would otherwise. And the temperature difference between the plates
will be higher with the baffles than without them. Perhaps some kind
of story justifying your claim of increased entropy increase can be
constructed from that. But, off the top of my head, I don't see how,
since we are still transferring the same amount of heat in the two cases.

So what am I missing here? How are your conjectures intuitively obvious?
What is varying and what is being held constant in your conjecture?


.

Relevant Pages

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