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Collector
Posts: 4172
Joined: August 21st, 2001, 12:37 pm

Cuchulainn:
better is "Unified Probability" is any number $p$ that satisfies $-\infty \leq p \leq \infty$
Saves a lot of hassle.

it subsumes all others.

can we quote you on this probability theory? quite liberal. everything is possible kind of attitude! New Age movements will love it.
Last edited by Collector on December 4th, 2018, 7:31 pm, edited 1 time in total.

Cuchulainn
Topic Author
Posts: 58957
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:

Cuchulainn:
better is "Unified Probability" is any number $p$ that satisfies $-\infty \leq p \leq \infty$
Saves a lot of hassle.

it subsumes all others.

can we quote you on this probability theory? quite liberal. everything is possible kind of attitude! New Age movements will love it.
World Peace as well

bearish
Posts: 4571
Joined: February 3rd, 2011, 2:19 pm

Cuchulainn:
better is "Unified Probability" is any number $p$ that satisfies $-\infty \leq p \leq \infty$
Saves a lot of hassle.

it subsumes all others.

can we quote you on this probability theory? quite liberal. everything is possible kind of attitude! New Age movements will love it.
Now, consider two independent events, each occurring with probability q. The probability of the joint occurrence of the two is given by p. If p is given by -1, what is q?

ppauper
Posts: 70239
Joined: November 15th, 2001, 1:29 pm

better is "Unified Probability" is any number $p$ that satisfies $-\infty \leq p \leq \infty$
Saves a lot of hassle.

it subsumes all others.

katastrofa
Posts: 7569
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

"W is sometimes called the "thermodynamic probability" since it is an integer greater than one, while mathematical probabilities are always numbers between zero and one" wiki
That is an odd usage. It’s like saying that the probability of rolling two dice whose sum is 11 is 2, rather than dividing through by the total number of equiprobable states to get 2/36, which is a proper probability.
Let me womansplain. The term "thermodynamic probability" is supposed to give an idea if a certain macrostate will occur in Nature. As an example imagine a box full of gas particles. Thermodynamic forces make the particles fill the box uniformly so that the same number of particles sits in the left and the right halves of the box. This is a macrostate. The n distinguishable particles can be rearranged in the box in ${n\choose 2}$ ways/microstates and it's still the same macrostate. Another macrostate can be when one particle sits in the left half and the rest is squeezed in the right half - it seems uncanny, but there are still n microstates realising such a macrostate. Thus, thermodynamic probabilities of those macrostates are ${n\choose 2}$ and n. The higher thermodynamic probability of the uniform macrostate means that it is more thermodynamically likely to occur.

This also means that a system converging to its equilibrium (which is defined as the macrostate with the highest thermodynamic probability - the uniform macrostate in this case) is maximising its entropy S, because S = k_B ln W (someone wrote this formula on Boltzmann's grave even if he never used it himself - yet another proof that physics is a lie). And this also means that the information we have about the system is decreasing towards the equilibrium, because when we observe the system we can see the macrostate only and not the particular microstate, which currently realises it. The more possible microstates, the less certain we can be which one makes up the macrostate. That's where information theory begins.

If you start to analyse the dynamics of the problem, you can ask which transition is more probable: from the first to the second microstate or vice versa? The difference of their thermodynamic probabilities gives you the answer, and eventually leads to defining reversible v irreversible processes... and the theory of ergodicity.

And so goes physics - sometimes it's not complete nonsense (or at least they managed to tweak it in such a way that it's hard to falsify - it's, as Cuchulainn's favourite goes, "not even wrong")...
Last edited by katastrofa on December 5th, 2018, 11:33 am, edited 3 times in total.

ppauper
Posts: 70239
Joined: November 15th, 2001, 1:29 pm

No you Kant: Russians reject German thinker's name for airport

Kaliningrad was Kant's home when the Baltic city was Prussian Königsberg.

bearish
Posts: 4571
Joined: February 3rd, 2011, 2:19 pm

"W is sometimes called the "thermodynamic probability" since it is an integer greater than one, while mathematical probabilities are always numbers between zero and one" wiki
That is an odd usage. It’s like saying that the probability of rolling two dice whose sum is 11 is 2, rather than dividing through by the total number of equiprobable states to get 2/36, which is a proper probability.
Let me womansplain. The term "thermodynamic probability" is supposed to give an idea if a certain macrostate will occur in Nature. As an example imagine a box full of gas particles. Thermodynamic forces make the particles fill the box uniformly so that the same number of particles sits in the left and the right halves of the box. This is a macrostate. The n distinguishable particles can be rearranged in the box in ${n\choose 2}$ ways/microstates and it's still the same macrostate. Another macrostate can be when one particle sits in the left half and the rest is squeezed in the right half - it seems uncanny, but there are still n microstates realising such a macrostate. Thus, thermodynamic probabilities of those macrostates are ${n\choose 2}$ and n. The higher thermodynamic probability of the uniform macrostate means that it is more thermodynamically likely to occur.

This also means that a system converging to its equilibrium (which is defined as the macrostate with the highest thermodynamic probability - the uniform macrostate in this case) is maximising its entropy S, because S = k_B ln W (someone wrote this formula on Boltzmann's grave even if he never used it himself - yet another proof that physics is a lie). And this also means that the information we have about the system is decreasing towards the equilibrium, because when we observe the system we can see the macrostate only and not the particular microstate, which currently realises it. The more possible microstates, the less certain we can be which one makes up the macrostate. That's where information theory begins.

If you start to analyse the dynamics of the problem, you can ask which transition is more probable: from the first to the second microstate or vice versa? The difference of their thermodynamic probabilities gives you the answer, and eventually leads to defining reversible v irreversible processes... and the theory of ergodicity.

And so goes physics - sometimes it's not complete nonsense (or at least they managed to tweak it in such a way that it's hard to falsify - it's, as Cuchulainn's favourite goes, "not even wrong")...
Thank you! Although you briefly had me feel empathy for the one particle sitting all by itself in the left half.

Cuchulainn
Topic Author
Posts: 58957
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:

As an example imagine a box full of gas particles

Like teaching Evolution to a creationist.

Cuchulainn
Topic Author
Posts: 58957
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:

No you Kant: Russians reject German thinker's name for airport

Kaliningrad was Kant's home when the Baltic city was Prussian Königsberg.
And where graph theory was born.

ppauper
Posts: 70239
Joined: November 15th, 2001, 1:29 pm

No you Kant: Russians reject German thinker's name for airport

Kaliningrad was Kant's home when the Baltic city was Prussian Königsberg.
And where graph theory was born.
I remember a post about the bridges
Still, I suspect the Russians don't want to remind people that Kalingrad was Prussian Königsberg until they took possession of it after WW2
On August 29, 1944, Soviet troops reached the border of East Prussia. By January 1945, they had overrun all East Prussia except for the area around Königsberg. Many inhabitants fled west at this time. During the last days of the war, over two million people fled before the Red Army and were evacuated by sea. The remaining population of 300,000 people were condemned to forced labour. Under the terms of the Potsdam Agreement, the city became part of the Soviet Union pending the final determination of territorial questions at a peace settlement. This final determination never took place.

katastrofa
Posts: 7569
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

That is an odd usage. It’s like saying that the probability of rolling two dice whose sum is 11 is 2, rather than dividing through by the total number of equiprobable states to get 2/36, which is a proper probability.
Let me womansplain. The term "thermodynamic probability" is supposed to give an idea if a certain macrostate will occur in Nature. As an example imagine a box full of gas particles. Thermodynamic forces make the particles fill the box uniformly so that the same number of particles sits in the left and the right halves of the box. This is a macrostate. The n distinguishable particles can be rearranged in the box in ${n\choose 2}$ ways/microstates and it's still the same macrostate. Another macrostate can be when one particle sits in the left half and the rest is squeezed in the right half - it seems uncanny, but there are still n microstates realising such a macrostate. Thus, thermodynamic probabilities of those macrostates are ${n\choose 2}$ and n. The higher thermodynamic probability of the uniform macrostate means that it is more thermodynamically likely to occur.

This also means that a system converging to its equilibrium (which is defined as the macrostate with the highest thermodynamic probability - the uniform macrostate in this case) is maximising its entropy S, because S = k_B ln W (someone wrote this formula on Boltzmann's grave even if he never used it himself - yet another proof that physics is a lie). And this also means that the information we have about the system is decreasing towards the equilibrium, because when we observe the system we can see the macrostate only and not the particular microstate, which currently realises it. The more possible microstates, the less certain we can be which one makes up the macrostate. That's where information theory begins.

If you start to analyse the dynamics of the problem, you can ask which transition is more probable: from the first to the second microstate or vice versa? The difference of their thermodynamic probabilities gives you the answer, and eventually leads to defining reversible v irreversible processes... and the theory of ergodicity.

And so goes physics - sometimes it's not complete nonsense (or at least they managed to tweak it in such a way that it's hard to falsify - it's, as Cuchulainn's favourite goes, "not even wrong")...
Thank you! Although you briefly had me feel empathy for the one particle sitting all by itself in the left half.
You're the only true man in this forum.

bearish
Posts: 4571
Joined: February 3rd, 2011, 2:19 pm

Let me womansplain. The term "thermodynamic probability" is supposed to give an idea if a certain macrostate will occur in Nature. As an example imagine a box full of gas particles. Thermodynamic forces make the particles fill the box uniformly so that the same number of particles sits in the left and the right halves of the box. This is a macrostate. The n distinguishable particles can be rearranged in the box in ${n\choose 2}$ ways/microstates and it's still the same macrostate. Another macrostate can be when one particle sits in the left half and the rest is squeezed in the right half - it seems uncanny, but there are still n microstates realising such a macrostate. Thus, thermodynamic probabilities of those macrostates are ${n\choose 2}$ and n. The higher thermodynamic probability of the uniform macrostate means that it is more thermodynamically likely to occur.

This also means that a system converging to its equilibrium (which is defined as the macrostate with the highest thermodynamic probability - the uniform macrostate in this case) is maximising its entropy S, because S = k_B ln W (someone wrote this formula on Boltzmann's grave even if he never used it himself - yet another proof that physics is a lie). And this also means that the information we have about the system is decreasing towards the equilibrium, because when we observe the system we can see the macrostate only and not the particular microstate, which currently realises it. The more possible microstates, the less certain we can be which one makes up the macrostate. That's where information theory begins.

If you start to analyse the dynamics of the problem, you can ask which transition is more probable: from the first to the second microstate or vice versa? The difference of their thermodynamic probabilities gives you the answer, and eventually leads to defining reversible v irreversible processes... and the theory of ergodicity.

And so goes physics - sometimes it's not complete nonsense (or at least they managed to tweak it in such a way that it's hard to falsify - it's, as Cuchulainn's favourite goes, "not even wrong")...
Thank you! Although you briefly had me feel empathy for the one particle sitting all by itself in the left half.
You're the only true man in this forum.
Aww - blushing furiously. And trying to think of something clever to say involving my cave.

katastrofa
Posts: 7569
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

I would definitely bring some vegan cookies for you and Mrs. Bearish. Lucky woman, and certainly very special herself.
Last edited by katastrofa on December 6th, 2018, 4:09 pm, edited 1 time in total.

Cuchulainn
Topic Author
Posts: 58957
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:

I remember a post about the bridges
Like Euler circuits, what goes around, comes around.

Cuchulainn
Topic Author
Posts: 58957
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:

The Philosophy of pseudo-profound BullShit (I thnk Alan was the the original poster (of the link, not the BS))

http://journal.sjdm.org/15/15923a/jdm15923a.pdf

Wilmott.com has been "Serving the Quantitative Finance Community" since 2001. Continued...

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