boltzmann

The Boltzmann Lament

No greater love, some chemists say,
than that of Boltzmann and his k.
The constant made him quite afflicted
and to an early grave (he self-inflicted).

How can we live with this duplicity
in a world of endless multiplicities?
I once tried to clean my room, you see,
But the universe increased its entropy.

Could anyone ever truly follow
such a sad lifetime full of sorrow?
For we’re all alone with these notations,
even with Maxwell’s relations. 

And oh, what would good old NIST
possibly begin to think about of all this?
But alas, there was nowhere to start
for questions put forth by the heart.

We’re star-crossed lovers, pchem and I,
And I understand why Boltzmann cried.
When asked if I would marry, would I say yes?
I could only yell my reply: VdP plus TdS!

I couldn’t stop, I couldn’t end it,
What’s the use, I cannot mend it!
I am feeling warm, I need a refresher.
What was constant, temperature or pressure?

Oh, the probability density may disappoint,
But I get faint at the thought of the triple point.
And energies, like jewels, they sing to me.
Especially in exponent, divided by kT.

They said, are you hungry? You look faint ‘round the eyes.
I looked up from my work, full of surprise.
I could not eat in all my frustration
when calculating the partition for vibration. 

“Electronic, translation, rotation!” I gasped.
Each was more beautiful than the last.
And with gases ideal, I knew what to do.
The free energy was minus kT ln of Q. 

I think the spirit of Boltzmann has me possessed
For I spent two weeks deciding which I liked best,
those energies, potential or kinetic.
I think these problems are genetic.

Boltzmann, soon we shall meet,
Hand in hand, Einstein we shall greet.
In the meantime, though, I’ve got just the ticket:
Let’s apply Arrhenius to those hyper crickets.


By: Maria Moutsoglou, entangled
For Dr. Hirko’s spring 2012 graduate statistical mechanics/thermodynamics course. 

Requested by punnybones

When a volcano erupts, it turns the sky gray with its ash, blocking out the sun and transforming the atmosphere into a cold, dark cloud of gas.

Luckily for any pokémon, when this happens, Volcarona appears, and acts as a perfect replacement for the sun.

As you can imagine, the sun’s not an easy thing to replace. If Volcarona wants to nab a job interview for the position of “Sun”, it better put a few good qualifications on its resumé.

First, let’s talk about distance. If Volcarona is a perfect replacement for the sun, we expect it to be identical in relative size, brightness, and temperature. When you look into our sky, the sun (because its so far away), has about ½ a degree of diameter across the sky. The sun’s actual diameter is about 1,391,684 km. Volcarona, who is only 1.6 meters tall, must be a lot closer for that effect. Volcarona is 869802500x smaller than the sun, so must be 869802500x closer to appear the same. 

Volcarona flies at about 171 meters (560 ft) above the planet’s surface to look the same size as the sun.

Now for brightness. It’s important to understand what Astronomers mean by luminosity. Brightness is quantified over all wavelengths, not just the ones we humans can see. So even though the sun emits lots of visible and ultraviolet waves, Volcarona probably emits more photons at infrared levels.

Furthermore, there’s a difference between apparent and absolute brightness. Apparent Brightness is how bright something looks to us, from Earth. For the sun (and for Volcarona), its about -26.7. Absolute Brightness is at a fixed distance (1 parsec). For the sun, it’s 4.83. You can imagine, because Volcarona is so much closer, it’s not nearly as bright, even if it looks the same. 

Volcarona has a absolute brightness of M=49.6, over 500,000,000,000,000,000x less bright than the sun. This corresponds to a Luminosity of 480 million Watts.

Of course, the more important thing about our sun is the heat we gain from it. Our sun is a lot hotter near its atomic-fusion core than it is at its surface, but overall the sun can be treated as one uniform body with an effective temperature or 5780 K (5507 C / 9944 F). Since we have the luminosity, we can find the temperature using a variation of the Stefan-Boltzmann Law,

Volcarona’s temperature is 5700 K / 9800 F / 5400 C.

This is interesting, because it’s almost the exact same as the effective temperature of the sun. Volcarona is a lot closer, smaller, and a lot less bright, but has the same temperature. Of course, there’s no way Volcarona could survive with this, but if it wants to replace the sun, that’s what it has to do.

The general struggle for existence of animate beings is not a struggle for raw materials – these, for organisms, are air, water and soil, all abundantly available – nor for energy which exists in plenty in any body in the form of heat, but a struggle for [negative] entropy, which becomes available through the transition of energy from the hot sun to the cold earth.
—  L., Boltzmann, (rev. 1974). The Second Law of Thermodynamics.
2

The first person to determine the surface temperature of the Sun (and to come up with a sensible result) was a Slovene physicist (also mathematician and poet) Jožef Stefan [ˈjoːʒɛf ˈʃteːfan]. His result of 5700K differs by only 80K from the modern estimate (5780K).

He calculated it using the formula j*=σT4 known as the Stefan–Boltzmann law, (which he first formulated in 1879, his student Ludwig Boltzmann later expanded its application in 1884), σ being the Stefan–Boltzmann constant (also known as only Stefan’s law and Stefan’s constant). He’s the only Slovene scientist to have a law of nature named after him (but other things have been named after him as well, including a crater on the Moon).

Mária

Mikor meghallotta a kocsmában az öregeket arról beszélni, hogy elküldtük a hadüzenetet a szerbeknek, Mária leejtette az egyik vizeskorsót. Szedegette a cserépdarabokat, és csak annyit tudott kinyögni:

- A mi laktanyákból is? - és érezte, hogy könnyel telik meg a szeme. Takács bácsi, akinek ugyan Gyulafirátót felé voltak a földjei, mégis mindig átjárt kocsmázni Máriáékhoz, felé fordult és azt mondta:

- Innen is mennek, Marika, hogyne mennének éppen Hajmáskérről, amikor ezek a legjobb tüzérek az egész Monarchiában.

Mária nem tudta, mit mondjon, csendben babrált a cserepekkel és sírt. Tudta, hogy Gábor hadnagy is elmegy, és talán nem is jön vissza soha, Gábor hadnagy ugyanis nem volt olyan ember, aki bármilyen harci tevékenységet képes lett volna túlélni. Amikor először találkoztak, Gábor hadnagy akkor is épp bocsánatot kérni jött, amiért szétrobbantotta a régi istállót, ahol Mária apja azokat a szerszámokat tartotta, amikkel már úgysem tudott dolgozni. Na meg egy nagy rakás szénát, úgyhogy égett is rendesen a rozoga épület.

- Nem tudtam, bocsánat, nem jól számoltam, ennek el kellett volna repülnie legalább a dombokon túlra - hajtogatta Gábor hadnagy, ahogy szaladt a lángoló istálló felé, de úgy tűnt, nem is Máriához és a szüleihez beszél, inkább saját magához. - Még legalább egy giroszkópot bele kell tenni a megfelelő irányításhoz, hajtóanyagból pedig sokkal több kellett volna. Majdnem jó már. Majdnem jó már.

Mária apja soha nem mert gorombán beszélni a Császári és Királyi Haderő egyetlen tisztjével sem, Gábor hadnagytól is csak annyit kérdezett:

- Aztán ki lesz-e fizetve?

- Ki lesz, bátyám, az utolsó fillérig, méghozzá a saját zsebemből - vakargatta a fejét Gábor hadnagy. - Az én pénzemből, ez ugyanis, hogy is mondjam, nem hivatalos Császári és Királyi lövegből jött.

- Hanem honnan? - kérdezte Mária.

- Ez, kisasszony, közvetlenül a körletemből jött, löveg nélkül, onnan, a laktanyából - Gábor hadnagy a tüzérségi laktanya felé mutatott, de az épületnek csak a tornyát lehetett látni jó messzire, a falu másik végén.

Aztán Gábor hadnagy elkezdett magyarázni arról, hogy feltalál egy fegyvert, amivel a Monarchia legyőzhetetlen lesz, egy olyan fegyvert, amihez nem kell löveg, és nagyon-nagyon messzire is elszáll. Mária nagyjából ennyit értett meg Gábor hadnagy szavaiból, a többit inkább csak megjegyezte. Például rengetegszer mondta azt a hadnagy, hogy “hajtóanyag” meg hogy “nem hiába, a nagy Boltzmann és Ciolkovszkij jól megmondták”.

Hat hónap múlva Gábor hadnagy azzal állított be Mária apjához, hogy megépített egy működő rakétát, és hogy adja hozzá feleségül a lányát. Az apja igent mondott, Mária pedig két héten keresztül a fellegek között járt.

Aztán jött az este, amikor az öregek arról beszélgettek, hogy elküldtük a hadüzenetet a szerbeknek, és Mária leejtette a vizeskancsót.

A lány a kocsmából egyenesen a laktanyába szaladt, Gábor hadnagy körletébe, és kérte, hogy hívják ki hozzá a vőlegényét. Gábor hadnagy egyenruhában, mosolyogva érkezett, és egy embermagasságú vashengert görgetett maga előtt.

- Marikám, erre neked kell vigyáznod, amíg nem vagyok itt. Rólad neveztem el, az a neve, hogy Mária-2. Mária-1 sajnos a körletben meghibásodott, és szét kellett szedni, különben felrobbant volna az egész laktanya. De Mária-2 tökéletesen működőképes - mondta büszkén.

Mária nem tudta, mit kezdjen a vashengerrel, de nem is ez érdekelte.

- Nekem csak az kell, hogy maga itt maradjon - szipogott, de Gábor hadnagy nem törődött vele.

- Most elmegyünk, a szerbeket szétvágjuk, visszajövünk, és Mária-2-t beterjesztem a Bizottságnak. A Monarchia legyőzhetetlen lesz, Mária! Mi leszünk az egyetlenek, akiknek stabil és irányítható rakétája van. Neked és nekem pedig annyi pénzünk lesz, hogy meg sem fogjuk tudni számolni.

Másnap Gábor hadnagy elment a frontra. Három hét múlva jött a hír, hogy lelőtték. Mária kezét egy évre rá megkérte egy hajmáskéri gazda, akinek nem kellett bevonulnia. Mire a gazdát a Tanácsköztársaság idején felakasztották, Mária már a két közös gyereküket nevelte.

De az embermagasságú vashengert soha nem engedte. Haláláig ott állt az ágya mellett Mária-2, ami tökéletesen működőképes.

The Brotzman Siblings

I think the Brotzman siblings definitely have a connection to the Boltzmann brains. In fact, I think that the Brotzman’s are the Boltzmann brains.

For you to understand:

“In physics thought experiment, a Boltzmann brain is a self-aware entity that arises due to extremely rare random fluctuations out of a state of thermodynamic equilibrium. For example, in a homogeneous Newtonian soup, theoretically by sheer chance all the atoms could bounce off and stick to one another in such a way as to assemble a functioning human brain (though this would, on average, take vastly longer than the current lifetime of the Universe).” (~ Wikipedia)

Boltzmann brains are self-aware entities (@ “I am the conciousness that controls the body of, sees through the eyes of, and hears the thoughts of Amanda Brotzman.”) different from normal human brains and can shape the world around them (Like when Amanda created the knife). But most importantly, they’re connected to the fabric of the universe.

Following that theory, I think that all the holistics are technically Boltzmann brains, connected to the fabric of the universe and their ‘conciousness’ can’t really die, like Dirk got his talent from his mother (the world needs those Boltzmann brains to keep it working and in the right order). But Todd and Amanda are the strongest of them, chosen in a time when they were needed the most and since they were in the backstage of reality, I guess they have the strongest connection to the universe/fabric of reality.

Whether to treat a system whose behavior you can’t predict in practice as deterministic or indeterministic in principle is a matter of convenience or preference. You can always model it at the level of coarse-graining determined by your own capabilities to observe and intervene on the system, or fine-grain - add hypothetical degrees of freedom to your model - until you have a deterministic model.

The former route is the traditional one taken in quantum mechanics - it’s an empirical fact that the behavior of quantum systems is unpredictable, given our current ability to observe and manipulate them, so most interpretations of quantum mechanics are indeterministic. The latter route is taken by deterministic hidden variable theories of quantum mechanics, such as the de Broglie-Bohm interpretation, where the hypothetical degrees of freedom are simply the particle positions.

A classic example of the ultimate success of the fine-graining approach in physics is the kinetic theory of gases (and more generally the transition from thermodynamics to statistical mechanics), developed well in advance of our ability to experimentally detect or manipulate molecular systems. The first quantitative kinetic theory of gasses was probably Daniel Bernoulli’s Hydrodynamica in 1738 (although interesting qualitative statements can be found in Lucretius’s De Rerum Natura from the 1st century BC). Convincing evidence of the molecular nature of matter came from Einstein’s theory of Brownian motion in 1905 (and its subsequent empirical confirmation by Chaudesaigues in 1907 and Perrin in 1908). In the meantime, as late as 1897, you had respectable physicists like Ernst Mach proclaiming that atoms and molecules were no more than a convenient fiction, forever beyond our ability to observe or manipulate.

Essentially Bernoulli, Maxwell, Boltzmann, and other people who developed the kinetic theory were saying that if gasses were made of lots of little molecules bouncing around according to deterministic Newtonian laws - if those hypothetical (particle position and momentum) degrees of freedom existed - then their large-scale, coarse-grained behavior would be consistent with what is empirically known about their (macroscopic) thermodynamics, including the unpredictable Brownian motion of dust motes in air. Until the 20th century, it was unclear whether empirical confirmation of the kinetic theory was even possible in principle, but in this instance the technique of deterministic fine-graining for describing the unpredictable phenomenon of Brownian motion (as opposed to indeterministic, stochastic techniques, which were also developed) led to the confirmation of the molecular theory of matter.

(brought to you by my patrons)

tfw you try to divide minimum word count by number of chapters but forget to notate the former properly so Google thinks you want an equation involving the Boltzmann constant