2nd Thermo Law

[Wiccan_Child]

Hey, Wiccan_Child, you had asked about my use of the term information function... I answered in post #59. Did you see it?

Ah, I did not. I'm off to play poker as it happens (what a life, eh), but I've got a tab open with a reply ready to be typed. Sorry for missing it!

Same goes for you, Resha. Posts all round!

 

[chilehed]

Well, some Christians claim he is unknowable and then turn around and describe him to me.

I'm sure they do. But nonetheless Christian theology does not hold that God is utterly unknowable.

I don't believe there is an ongoing process by which entropy is decreasing. I believe entropy is increasing, in fact.

As I recall the question of the OP was about whether or not there is a reason to think that there might be QM processes which result in an entropy generation less than zero.

 

[Wiccan_Child]

In my career I've had several texts on thermodynamics, and all of them give the Clausius statement as some variant of "It is impossible for a self acting machine working in a cyclic process without any external force, to transfer heat from a body at a lower temperature to a body at a higher temperature." The Kelvin-Plank statement is given a similar formulation.

According to this online copy of an 1879 translation of Clausius' original work, his statement arises during his discussion of cyclic processes, and is specifically formulated as such:

This Principle may be expressed in words as follows: If in a reversible Cyclical Process every element of heat taken in positive or negative be divided by the absolute temperature at which it is taken in and the differential so formed be integrated for the whole course of the process the integral so obtained is equal to zero ​

The mechanical theory of heat - Google Books See page 90.

In any case, the formulation given in my college textbook is correct. It is impossible for a self acting machine working in a cyclic process without any external force, to transfer heat from a body at a lower temperature to a body at a higher temperature. But it's not the most general formulation, and it doesn't imply that the Second Law applies only to cyclic processes.

Yes, the law as you state it is true: the entropy of closed systems do behave in that way. But that's not the most general formulation of the Law, and to insist that it means that the Law applies only to closed systems is to make the same type of error as one who insists that the Law only applies to cyclic processes.

Well yes, I was being facetious One translation of the Claudius statement isn't the only valid one.

Yeah, it's complicates things when people hijack the language.

In statistical mechanics, entropy is given by

S = -kB *∑[sub]1[/sub][sup]i[/sup](ρ[sub]i[/sub] * ln(ρ[sub]i[/sub]))​

in which ρ[sub]i[/sub] is the probability of each microstate available at the macrostate in question and kB is Boltzman's constant.

In information theory, -∑[sub]1[/sub][sup]i[/sup](ρ[sub]i[/sub] * ln(ρ[sub]i[/sub])) is known as the information function.

The most generalized statement of the Second Law is

"In every real thermodynamic process, delta(S) = -kB * delta(∑[sub]1[/sub][sup]i[/sup](ρ[sub]i[/sub] * ln(ρ[sub]i[/sub]))) >/= 0​

So then the statements "entropy increases" and "the information function increases" are exactly equivalent, and when a YEC says that evolution results in an increase in information then he's conceded that it complies with the Second Law. But he might be unaware of that or unwilling to admit it.

In my experience, it's usually the former - they have a severe misunderstanding of both information (as it applies to thermodynamics) and the Second Law, equating 'entropy' with 'complexity' with 'God', bizarrely.

Thanks for the information on information functions, though

That's something new for me.

 

[chilehed]

As I recall the question of the OP was about whether or not there is a reason to think that there might be QM processes which result in an entropy generation less than zero.

I just realized that my thinking's been a bit sloppy... gimme a bit to collect my thoughts. A couple of days, probably, considering how busy my weekends are. I'll be interested in everyone's comments on what I have.

 

[chilehed]

Unfortunately I won't be able to properly collect and rigorously present my thoughts in a timely manner, I've just been too busy. But the short version is:

1. QM fluctuations will zero effect on a system's entropy, because as the system approaches scales at which the Second Law is applicable, the average of such fluctuations approachs zero.

2. The phrases "lowering the entropy of a system" and "rendering a system's heat more available to do work" are not synonymous.

3. There is no functional difference between an open system and a closed system working on a cycle; one can be turned into the other merely by moving the system boundaries slightly. The expansion valve in a heat pump serves the same function as does the open environment between the outlet and inlet of a jet turbine engine.

4. You have to be very careful that you don't redefine the macrostate in the middle of the analysis.​