# 2LOT and ID entropy calculations (editorial corrections welcome)

Some may have wondered why me (a creationist) has taken the side of the ID-haters with regards to the 2nd law. It is because I am concerned for the ability of college science students in the disciplines of physics, chemistry and engineering understanding the 2nd law. The calculations I’ve provided are textbook calculations as would be expected of these students.

The fundamental problem is 2LOT is concerned with energy (or position/momentum) microstates, whereas IDists are concerened with “design space” microstates. The number of microstates can both be expressed in information bits, but it does not mean we are dealing with the same microstates. I’m providing sample calculations to prove the point that it is disastrous for IDists to invoke textbook 2LOT for the simple reason 2LOT is concerened with energy (or position/momentum) microstates which has little or nothing to do with “design space” microstates of interest to ID.

I’m going through textbook thermodynamics here. If we have 500 fair copper pennies, how many “design space” microstates are there? Standard ID answer:

2^500

since there are 500 coins and each coin has 2 states, a system of 500 coins then has 2^500 possible symbolic configurational states or microstates. This can also be expressed in bits:

I_design_space = – log2( 1/ (2^500) ) = 500 bits

What is the design space entropy?

I_design_space = S_design_space = 500 bits

IN CONTRAST, how many thermodynamic energy microstates are there in this system of 500 pure copper pennies at standard “room” temperature (298 Kelvin). The textbook style calculation is as follows:

Mass of a copper penny 3.11 grams.
Molar weight of copper 65.546.
Standard molar entropy of copper 33.2 J/K/mol.

Thermodynamic entropy of 500 copper pennies is therefore:

S_thermodynamic = 500 * 33.2 Jolues/Kelvin/Mol * 3.11 grams 65.546 grams/ mol = 826.68 J/K

The thermodynamic entropy in J/K can be converted to bits by simply dividing by Boltzman’s constant and then converting the natural log measure to log-base-2 measure.

Boltzmann’s constant is 1.381x 10-23 J/K).
The natural log to log-base-2 conversion is ln(2) = .693147.

Thermodyamic entropy in bits is computed as follows:

S_thermodynamic = I_thermodynmic =826.86 J/K = 826.68 J/K / (1.381x 10^-23 J/K) / .693147 = 8.636 x 10^25 bits

The number of thermodynamic microstates is simply taking 2 raised to the power of I_thermodynmic

2^(8.636 x 10^25)

which is a GIGANTIC number.

Clearly the design space entropy is not the same as the thermodynamic entropy because the design space microstate is not the same as the thermodynamic microstate.

Now let us heat the coins from room temperature to near boiling of water (373 Kelvin). What is the change in entropy or the number of microstates?

At 373 Kelvin the “design space” entropy is still 500 bits since the possible number heads tails microstates does not change with this increase in temperature.

However the thermodynamic entropy and thermodynamic microstates change. What is the change in entropy? Again using standard textbook thermodynamics.

Specific heat of copper 0.39 J/gram
Heat capcity C of 500 copper pennies:

C = 0.39 J/gram/K * 500 pennies * 3.11 grams/penny/K = 606 J/K

T_initial = 298 K
T_final = 373 K

To calculate the change in entropy I used the formulas from:
http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node41.html

delta-S_thermodynamic = C ln ( T_final/T_initial) = 606 J/K ln (373/298) = 136.13 J/K

Total thermodynamic entropy is calculated as follows:

S_thermodynamic_initial = 826.86 J/K

S_thermodyanmic_final = S_thermodyanmic_initial + delta-S_thermodynamic = 826.86 J/K + 136.13 J/K = 963.0 J/K

Again we can convert this to bits using procedures similar to the above conversions:

S_thermodyanmic_final = 963.0 J/K = 963.0 J/K / (1.381x 10-23 J/K) / .693147 = 1.01 x 10^26 bits

The ADDED number of microstates due to the increase in temperature is calculated as follows:

delta-S_thermodynamic = 136.13 J/K = 136.13 J/K / (1.381x 10^-23 J/K) / .693147 = 1.42 x 10^25 bits

Thus the number of thermodynamic microstates added by heating is simply found by rasing 2 to the power of delta-S_thermodynamic

2^delta-S_thermodyanmic = 2^(1.42 x 10^25)

Adding heat can be said to make the copper molecules bounce around more chaotically (disorderly if you will), and hence increase the thermodynamic entropy and microstates, but it says nothing of the change in design space entropy or microstates.

BOTTOM LINE:

Increasing heat increases the thermodynamic entropy and the individual copper molecules look more chaotic (disorderly if you will) because they are vibrating faster from the added heat, but it does nothing to change the design space entropy.

At 298 Kelvin:

Design Space Entropy: 500 bits
number of Design Space microstates: 2^500

Thermodyamic Entropy: 8.636 x 10^25 bits
number Thermodynamic microstates: 2^(8.636 x 10^25)

At 373 Kelvin by adding heat :
Design Space Entropy: 500 bits
number of Design Space microstates: 2^500
change in Design Space entropy due to heat change : 0 bits
change in number of Design Space microstate due to heat change: 0 microstates

Thermodyamic Entropy: 1.01 x 10^26 bits
number Thermodynamic microstates: 2^(1.01 x 10^26)
change in thermodynamic entropy due to heat change : 1.42 x 10^25 bits
change in number of thermodynamic microstates due to heat change: 2^(1.42 x 10^25) microstates

Moral of the story: don’t use 2lot to argue for design space entropy change. Besides, as pointed out earlier, increasing design complexity usually entails increase of both design and thermodynamic entropy.

Why all this obsession with reducing entropy to increase design complexity? I hope one can see it can be desirable to INCREASE entropy (both design and thermodynamic) in order to increase design complexity. A warm living complex human has more thermodynamic and design space entropy than a dead lifeless ice cube.

## 118 thoughts on “2LOT and ID entropy calculations (editorial corrections welcome)”

1. stcordova
Ignored
on said:

Keith’s “corrected” equation:

1 nat = (1.381x 10^-23 nat/(J/K))(J/K)

Hmmm, after the J/K’s cancel we have:

(1.381x 10^-23 nat/(J/K)) (J/K) = 1.381x 10^-23 nat

1 nat ≠ 1.381x 10^-23 nat

Hence your equality seems off by 1/(1.381x 10^-23), which is pretty big.

Me thinks you need to have a bigger appreciation for the law of non contradiction.

2. keiths
Ignored
on said:

Sal,

Hence your equality seems off by 1/(1.381x 10^-23), which is pretty big.

You’re right. I left out a constant, but that’s easily fixed. Everything else, including my conclusion — that J/K is not dimensionless, contrary to your claim — remains the same.

With the fix:

1 nat = (1.381 x 10^-23 J/K)(1 nat/1.381 x 10^-23 J/K)
200 ingots = (2000 kg)(1 ingot/10 kg)

The J/K terms cancel, leaving a result in nats. So both the LHS and RHS are dimensionless. The kg terms cancel, leaving a result in ingots. So both the LHS and RHS are dimensionless.

Going in the opposite direction,

1 nat /(1 nat/(1.381 x 10^-23 J/K)) = 1.381 x 10^-23 J/K
200 ingots/(1 ingot/10 kg) = 2000 kg

The nats cancel, so both the LHS and RHS are dimensioned. The ingots cancel, so both the LHS and RHS are dimensioned.

And again, removing ‘nat’ and ‘ingot’ from the equations doesn’t make any difference. They’re still implicit.

So the answer is no, I do not agree with your sloppy equation.

It’s time to admit your mistake and move on, Sal. J/K is not dimensionless.

You lost another one.

So unless you’re willing to argue that the kilogram is dimensionless, you’re stuck.

The kilogram is not dimensionless, and neither is J/K.

3. stcordova
Ignored
on said:

You’re right.

See, it’s not so hard to admit I was right about something. Penance is good for the soul. Kudos to you.

4. keiths
Ignored
on said:

Sal,

I have no problem admitting my errors, as you just witnessed..

Why can’t you admit yours? J/K is obviously not dimensionless, as my arguments show.

You got it wrong. Why aren’t you honest enough to admit that?

5. Richardthughes
Ignored
on said:

There’s a reason the “creation evolution university” died…

6. keiths
Ignored
on said:

Rich:

There’s a reason the “creation evolution university” died…

That’s not quite fair, Rich. There was some activity there just yesterday. And what do you know, it was Sal posting something entitled

Oops.

LMAO. 🙂

7. stcordova
Ignored
on said:

Being mistaken is not the same as being dishonest, I don’t think I’m mistaken.

I think this is legitimate when we are talking about thermodynamic entropy:

1 nat = 1.381x 10^-23 J/K

this implies the dimensionless conversion factor from J/K to nats:

1 = 1 nat / (1.381x 10^-23 J/K)

or letting nat =1,

1 = 1 / (1.381x 10^-23 J/K)

but you’re the one who said you don’t think:

1 nat = 1.381x 10^-23 J/K

is correct. You yourself said:

So the answer is no, I do not agree with your sloppy equation.

Which means you think this is wrong:

1 nat = 1.381x 10^-23 J/K

Suit yourself.

8. keiths
Ignored
on said:

Sal:

Being mistaken is not the same as being dishonest, I don’t think I’m mistaken.

Of course you’re mistaken, because your broken logic leads to the conclusion that kilograms are dimensionless. That’s just goofy, Sal.

9. stcordova
Ignored
on said:

I’d really like to thank Keiths for his patience and forbearance in answering my questions in a straight forward way such as saying this equation is a sloppy invention of mine, of moi:

1 nat = 1.381x 10^-23 J/K

But you know, it maybe I’m just slow and can’t see my error. If “my” equation is assumed as a premise, I concluded this:

1 nat = 1.381x 10^-23 J/K

1 = nat / (1.381 x 10^23 J/K) = 7.24×10^22 nats / (J/K) = DCF

where DCF means “Dimensionless Conversion Factor”

So presumably if I had 1 J/K I could apply this hypothesis and get a certain number of nats as follows:

1 J/K = 1 (J/K) DCF = 1 (J/K ) 7.24×10^22 nats / (J/K) =

7.24×10^22 nats

funny, this final figure looks like exactly the figure produce by this online calculator which I punch in 1 J/K and request a conversion to nats. Amazing coincidence, eh?

http://conversionai.com/unit/information-entropy/joules-per-kelvin-si-unit/nat-nip-nepit

So how again is “my” equation wrong? Guess I’m a bit slow today. I do appreciate you calling it “my” equation. Seems like I discovered a brand new physical insight with Sal’s Theorem :

1 nat = 1.381x 10^-23 J/K

Ah, but far be it for me to accept the credit you wish to bestow. I owe it all to Ludwig Botzmann and company. Thanks for the kind thought, but I can’t take credit for the equation.

10. keiths
Ignored
on said:

Sal:

I’d really like to thank Keiths for his patience and forbearance in answering my questions in a straight forward way such as saying this equation is a sloppy invention of mine, of moi:

1 nat = 1.381x 10^-23 J/K

But you know, it maybe I’m just slow and can’t see my error.

I’m happy to explain it again, but this time why not think about it rather than dashing off a hasty and ill-considered response?

The problem with saying

1 nat = 1.381 x 10^-23 J/K

is the same as the problem with saying

1 copper ingot = 10 kg .

They aren’t literally equal. You can’t substitute one for the other, willy-nilly.

Similarly,

1 dollar = 4 quarters

is not literally true. You can’t substitute one for the other at will. If your friend says that you owe her a dollar, she is not demanding four quarters from you. She’ll accept a dollar bill.

What those three sloppy equations really represent are equivalent and interconvertible representations.

1 nat, interpreted as an entropy, can be converted to 1.381 x 10^-23 J/K, and vice-versa.

1 copper ingot, interpreted as a mass, can be converted to 10 kg, and vice-versa.

1 dollar, interpreted as a monetary value, can be converted to 4 quarters, and vice-versa.

In each case we have two equivalent representations of the same underlying referent. Some are dimensionless, and others are not.

Your mistake is in thinking that if one representation is dimensionless (1 nat), then the other representation must also be dimensionless (1.381 x 10^-23 J/K).

That’s obviously false. If it were true, then the kilogram would be dimensionless by the same reasoning. One representation is dimensionless (1 ingot). By Cordova Logic, the other representation must also be dimensionless (10 kg). That’s clearly wrong, so Cordova Logic is rejected.

It’s a reductio ad absurdum.

J/K is not dimensionless for the same reason that the kilogram is not dimensionless.

Do you finally see (and admit) your mistake, Sal?

11. stcordova
Ignored
on said:

Let’s see here,

I claimed:

1 nat = 1.381x 10^-23 J/K

Keiths said I just made that up, that he doesn’t accept it, that is wrong, blah blah blah.

I then demonstrated credible evidence the above relation is utilized for conversions that are available elsewhere, not just in this discussion. Still no retraction by Keiths. Who’s making a mistake now?

Instead he as to argue using sloppily formed equalities like:

1 copper ingot = 10 kg

Where the proper way would have been

mass of 1 copper ingot = 10 kg

Clearly in this case, the phrase:

“1 copper ingot = 10 kg ”

is shorthand for

“mass of 1 copper ingot = 10 kg”, but he deliberately uses sloppy language to make this absurd looking statement, and then fallaciously attributes an argument I never made to me:

By Cordova logic:

200 ingots = 2000 kg

200 ingots/2000 = kg

The left hand side is dimensionless. Therefore, by Cordova logic, the kg is dimensionless.

But that’s what one has to resort to when losing an argument. Knocking down arguments I never made.

The proper argument would been something like this:

Mass of 200 ingots = 2000 kg

Mass of 200 ingots/2000 = kg

The left hand side is dimensioned in dimension of mass as is the right hand side.

J/K is a unit of entropy. Nat is a unit of entropy, therefore this relation which Keiths derided, but which I have proven as valid holds without equivocation:

1 nat = 1.381x 10^-23 J/K

The only way that would be invalid is if J/K is not a measure of entropy! Hence, no dice, Keiths, but thanks for responding directly to my questions. The mistakes is Keiths, and let me list them:

1. Keiths claims I made up the relation 1 nat = 1.381x 10^-23 J/K, (I did not)

2. the relation is wrong (it is right, I gave evidence it is correct by reference to conversion calculators, etc.)

3. his “corrected” equation was actually incorrect, it resulted in the absurdity
1 nat = 1.381x 10^-23 nats, it was so egregious after I pointed out, he had to capitulate lest I have more to hammer him with

4. Keiths insists J/K is not really a measure of entropy, like copper ingots aren’t really a measure of mass. Of course copper ingots aren’t a measure of mass, their mass (if standard to 10 kg) could be a measure of mass. It is the property of “mass of a standard mass copper ingot” that can be used as a measure of mass.

But Keiths is arguing as if J/K is not a measure of entropy, he’s trying to represent J/K as something that has a property that can be used to measure entropy. He is arguing, that J/K is in fact, not really a measure of entropy. That’s just plain wrong. If it is indeed true J/K is a measure of entropy and not just some property of J/K, then this relation is true without equivocation:

1 nat = 1.381x 10^-23 J/K

If we are measuring the entropy of a system, we can measure it in terms of nats or J/K.

And I have proof of this. See:

The SI unit for Entropy (S) is Joules per Kelvin (J/K)

http://en.wikibooks.org/wiki/Units_of_Measurement/Entropy

Keiths is essentially arguing J/K isn’t really measuring the same entropy that nats are measuring, that it is only some property of J/K that measures entropy much like some property of ingots (namely mass) that can be used as measure of mass. That’s just plain wrong.

12. keiths
Ignored
on said:

Sal,

I’ve noticed that the more desperate you become, the more likely you are to slip into your longstanding bad habits — like lying about your opponent’s position.

Lie #1:

I claimed:

1 nat = 1.381x 10^-23 J/K

Keiths said I just made that up, that he doesn’t accept it, that is wrong, blah blah blah.

No, I didn’t. I said was that “it wasn’t strictly correct” and that it was “sloppy”, and I explained exactly why.

Lie #2:

1. Keiths claims I made up the relation 1 nat = 1.381x 10^-23 J/K, (I did not)

Lie #3:

2. the relation is wrong (it is right, I gave evidence it is correct by reference to conversion calculators, etc.)

I didn’t say that. You just made it up.

Lie #4:

Keiths insists J/K is not really a measure of entropy, like copper ingots aren’t really a measure of mass.

No, I don’t. You just made that up.

Lie #5:

But Keiths is arguing as if J/K is not a measure of entropy,

No, I’m not. It is a measure of entropy — obviously.

Sal, you’ve demonstrated both your incompetence and your dishonesty to readers of this thread. I am happy to leave you in that unenviable position.

13. Richardthughes
Ignored
on said:

Some things don’t change, eh Sal? Jesus must be so proud!

14. stcordova
Ignored
on said:

Keiths’s selective memory:

I don’t equate them. You’re making stuff up again.

1 dimensionless nat = (1.381x 10^-23) (J/K)
…..

The ‘silly equality’ is yours, not mine.

I don’t equate them. You’re making stuff up again.

http://theskepticalzone.com/wp/?p=27185&cpage=2#comment-60616

Then Keiths complains:

I did, they are quoted above. You’re insinuating the equation is mine (as if it’s only mine, that I made it up).

You said you “don’t equate them”. What don’t you equate:

1 nat = (1.381x 10^-23) (J/K)

So do agree or not? You said:

So the answer is no, I do not agree with your sloppy equation.

http://theskepticalzone.com/wp/?p=27185&cpage=2#comment-60681

My equation. Moi?

Too funny. You don’t agree with that equation, you even referred to it as “your [Sal’s] sloppy equation”.

Still sticking to your story after I showed you that this “sloppy equation” predicts a conversion that apparently appears elsewhere outside of these discussions such as in an entropy conversion calculator?

And that was the same post you were called in the carpet for your “correct” equation. But this is a howler:

a dimensionless quantity can be converted to a dimensioned one, and vice-versa.

My copper ingot example shows exactly how it is done.

Thanks for a nice trophy Keiths. Your copper ingot example uses a false premise that is based on an equivocation.

15. stcordova
Ignored
on said:

Well, well, well, look at this Wiki entry:

nat ≡ kB = 1.380 650 5(23)×10^−23 J/K

http://en.wikipedia.org/wiki/Conversion_of_units

Does that look familiar?

I mean, I confess I rounded it off a bit, but it looks like something I’ve been sayin’ all along

1 nat = 1.381 x 10^-23 J/K

but nevertheless you said:

So the answer is no, I do not agree with your sloppy equation.

My sloppy equation? Moi?

The LHS has been declared as dimensionless, thus by inference the RHS must be dimensionless. As it says here:

Any physically meaningful equation (and any inequality and inequation) must have the same dimensions on the left and right sides.

If it is dimensionless on the LHS it must be so on the RHS.

You’re the one being idiosyncratic about all this, not me…

16. JonF
Ignored
on said:

If it is dimensionless on the LHS it must be so on the RHS.

Well, it’s certainly evident that the left side has dimensions, therefore nats have dimensions J/K.

Keep digging, this is hilarious.

17. Erik
Ignored
on said:
18. stcordova
Ignored
on said:

JonF,

Well, it’s certainly evident that the left side has dimensions, therefore nats have dimensions J/K.

Keep digging, this is hilarious.

I have the last laugh on you. There are dimensionless units. Haha! See:

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