# Tag Info

Accepted

### Derive Canonical Ensemble from Maximum Entropy Principle

A good way to start the proof is to first select some basis such that the density matrix $$\rho=\sum_{j}{p_j|\psi_j\rangle \langle\psi_j|}$$ where $p_j>0$ and $\{|\psi_j\rangle\}$ is orthonormal. ...
• 448

### Calculating dark energy

Theories and models in physics do not have a preferred mathematical base. The physical constants and properties of substances in a model can be written out in any base - in the same way as constants ...
• 33.9k
1 vote

### Gravitational path integral derivation of black hole temperature and entropy

You raise an excellent question in regards to how such thermodynamic quantities should be interpreted. That is, it is reasonable to ask why we attribute them directly to the black hole when we're ...
• 709

### What would "break" in reality if I had a perpetual motion device?

If you could have devices having 100% or even more than 100% energy efficiency , then you can easily break the first as well as second law of thermodynamics and cool your ice-cream while sitting ...
• 44

• 24.4k

### What is an intuitive explanation for $T = \mathrm{const}$ when $\Omega(E) = e^E$?

The basic intuition here is that temperature is not about number of microstates as such. Rather, it is about how the number of microstates varies with the energy---the standard definition of ...
• 47.1k
Accepted

### What is an intuitive explanation for $T = \mathrm{const}$ when $\Omega(E) = e^E$?

I'd say the relevant quantity here is $\omega (E):=\ln\,(\Omega (E)) = - \ln \,(1/\Omega(E))$. You can view $\omega$ as a measure of information or rather of missing information, in the sense of how ...
• 3,987
Accepted

### Confusion regarding the total number of microstates of a $N$ particle system

Note: it would be better to indicate the sum of the total microstates as $\Omega=\sum_{\{n_i\}}^* W{\{n_i\}}$, where $^*$ indicates that the sum is performed over the sets $\{n_i\}$ that satisfy the ...
### Why can't $pV$ work generate entropy in a reservoir?
Why can't $pV$ work generate entropy in a reservoir? The short answer is it can, if the $pV$ work is irreversible. Reversible work neither generates nor transfers entropy. So what it boils down to is ...