/sci/ - Science & Math

[Anonymous No.9817872]

>Let [math]\Sigma[/math] be a system which may exchange energy with the rest of the Universe.
>By second law of thermodynamics, [math]\mathrm dS\;=\;\frac{\delta Q}T\,+\,\delta S_\text c[/math] with [math]\delta S_\text e \;>\; 0\;\mathrm{J\;K^{-1}}[/math].
>By first law of thermodynamics, [math]\mathrm dU\;=\;\delta W\,+\,\delta Q[/math].
>Therefore, [math]\mathrm dS\;=\;\frac{\mathrm dU}T\,-\,\frac{\delta W}T\,+\,\delta S_\text c[/math]
>Suppose, for a moment, that [math]\mathrm dU\;=\;T\,\mathrm dS\,-\,p\,\mathrm dV[/math].
>Then, [math]\mathrm dS\;=\;\mathrm dS\,-\,\frac{p\,\mathrm dV}T\,-\,\frac{\delta W}T\,+\,\delta S_\text c[/math] i.e. [math]\delta S_\text c\;=\;\frac{p\,\mathrm dV}T\,+\,\frac{\delta W}T[/math].
>Now, decompose [math]\delta W[/math] into [math]\delta W_\text{alt}\,-\,p\,\mathrm dV[/math].
>Then, [math]\delta S_\text c \;=\; \frac{p\,\mathrm dV}T \,+\, \frac{\delta W_\text{alt}}T \,-\, \frac{p\,\mathrm dV}T \;=\; \frac{\delta W_\text{alt}}T[/math] i.e. [math]\delta W_\text{alt}\;=\;T\,\delta S_\text c[/math], henceforth the non-pressure work received by [math]\Sigma[/math] is only possible if entropy is being created.
>Then, by some handwavy use of Boltzmann's definition of entropy, we have that entropy has an upper bound of [math]k_\text B\,\ln\,\Omega[/math] where [math]\Omega[/math] is the number of elementary particles with a mass.
Is that really how heat death is proven? Cause it's bullshit. This whole thing is starting to smell like the Planck length meme.

[Anonymous No.9818032]

>>9817872
I don't care about this thread.

But why is Tex still broken? Get your shit together /sci/.

[Anonymous No.9818050]

>>9817872
>like the Planck length meme
Do you at least agree Something at small scales is quantized?

[Anonymous No.9818093]

In an effort to bump this thread out of interest and pull some bullshit out of my ass... Cosmology is the meme, assumptions galore. Gibbs free energy isn't even close to the worst one. You can derive the ideal gas law with [math]S=k_\text B\,\ln\,\Omega[/math]. i.e. not handwavy bullshit. Also you forgot about bosons.

[Anonymous No.9818176]

>This thread
Add a retarded Wojak and you get how I feel being here.

[Anonymous No.9818185]

>>9818176
sans gravity??
gimme a break...

whats the first term even?

[Anonymous No.9818218]

>>9818185
kinetic term for gluons

[Anonymous No.9818226]

>>9818218
>gluons
beyond the scope of my understanding...

whats the 2nd term?

[Anonymous No.9819230]

>>9818093
So basically, you're saying that the whole of cosmology relies on meaningless assumptions and is therefore popsci?

[Anonymous No.9819258]

>>9818226
Gluons interacting with each other I think

In any QFT lagrangian, it's a kinetic term (describes how it moves) if it only has two of the same field, and it's an interaction term if there are more fields interacting.

>>9819230
I did a little bit of cosmology last semester in GR class and basically the big cosmological models with analytic solutions are all about "Well if we assume that [thing that is only approximately true right now], then..."

[Anonymous No.9819289]

>>9817872

I think the more natural and modern perspective of entropy is that of information entropy. The view is that entropy isn't a real, physical quantity, and that statistical mechanics does not uniquely describe our physical world but represents states of knowledge of a system.

The information we have of a system can be thought of as the difference between the maximum possible entropy and it's current entropy, and using some basic properties that we'd expect the quantity 'information' to follow we naturally arrive at the [math]-\log[\rho][/math] formula. The total information is just taking the expected value by averages over all the probabilities [math]\rho[/math]

[Anonymous No.9819341]

is math the only hard science?