4
votes
3answers
177 views

Mathematical proof of the Second Law of Thermodynamics

Is there some book or paper that formalizes statistical mechanics, like some people have done with relativity, and proves the second law of thermodynamics from more foundational axioms?
3
votes
1answer
42 views

Problems with units of entropy in statistical thermodynamics

The statistical thermodynamics definition of entropy: $S = kN \ln (W)$ troubles me a lot with the problem of dimenstions. where $S$ is entropy; $k$, the Boltzmann constant; $N$ the number of particles ...
3
votes
3answers
156 views

Existence of negative temperatures and the definition of entropy

How negative temperatures can be possible has been treated on StackExchange before (several times in fact), but in light of some recent academic discussion, most of these answers seem to be possibly ...
3
votes
0answers
39 views

Is there a general H-theorem?

In statistical mechanics, Boltzmann showed that for dilute gases the H-function increases. I remember from a lecture that there is no general H-theorem, e.g. for non-dilute gases or in the quantum ...
4
votes
4answers
152 views

Question on entropy

All of my textbooks mention, that entropy-change of all spontaneous physical, and chemical processes is positive, and that such processes need another condition to fulfill- decrease in the net ...
2
votes
1answer
67 views

Entropy is constant. How to express this equation in terms of pressure and density?

In hydrodynamics of an ideal, non-compressive flow we use 5 variables: pressure $p$, density $\rho$ and velocity field $\mathbf{v}$. So we need 5 equations. Landau's "Hydrodynamics" states that the ...
3
votes
2answers
95 views

Quantum entropy in term of density matrix

Why in von Neumann expression of quantum entropy we have trace of density matrix expression? Why don't off diagonal term play a role?
1
vote
1answer
40 views

How can the microstates be measured with zero energy expenditure?

James P. Sethna. Statistical Mechanics. Exercise 5.2: What prevents a Maxwellian demon from using an atom in an unknown state to extract work? The demon must first measure which side of the ...
0
votes
1answer
41 views

Entropy and chemical potential of an ideal gas

I am reading Schroeder's book "Thermal Physics". One calculation in the text was not quite clear to me. The entropy of an ideal gas is given by the Sackur-Tetrode equation: $$ ...
6
votes
2answers
63 views

Classical and Semi-classical treatments of the ideal gas

In the semi-classical treatment of the ideal gas, we write the partition function for the system as $$Z = \frac{Z(1)^N}{N!}$$ where $Z(1)$ is the single particle partition function and $N$ is the ...
4
votes
0answers
67 views

Intuitively, why does removing solutes cost $k_B T$ of free energy per molecule?

I can calculate that if you want to, for example, desalinate water, you will have to pay a free energy cost of $k_B T$ for each ion you remove. In other words, removing an ion from a volume of water ...
1
vote
0answers
41 views

Is entropy a dynamical quantity [closed]

I am confused whether Entropy is a dynamical quantity or not. Gibbs entropy, and quantum mechanical Von Neumann entropy.
29
votes
7answers
3k views

Homemade salad dressing separates into layers after it sits for a while. Why doesn't this violate the 2nd law of thermodynamics?

The oil, vinegar and other liquids in homemade salad dressing separate into layers after sitting for a while, making the mixture become more organized as time evolves. Why doesn't this violate the ...
3
votes
1answer
100 views

Definition of Information in Information Theory

I am not sure in which SE site I have to put this question. But since I have learnt Shannon Entropy in the context of Statistical Physics, I am putting this question here. In the case of Shannon ...
0
votes
0answers
34 views

On the relationship between entropy and chaotic noise

I have few conceptual questions related to application of chaos in communications. Kolmogorov-Sinai Entropy1 , Kolmogorov-Sinai Entropy2 and Kolmogorov-Sinai Entropy3 KS is an entropy metric for ...
0
votes
2answers
63 views

Would it be possible to measure the change of entropy of a system? why?

To be more specific, what I mean is to measure it in a experiment. And if the answer is no, I want to know if it is principally impossible, or just impossible due to the technic limitation of our ...
8
votes
1answer
110 views

What precisely does the 2nd law of thermo state, considering that entropy depends on how we define macrostate?

Boltzmann's definition of entropy is $\sigma = \log \Omega$, where $\Omega$ is the number of microstates consistent with a given macrostate. If I understand correctly, this means that it only makes ...
3
votes
1answer
116 views

What is the resolution to Gibb's paradox?

This question is essentially a duplicate of Gibbs Paradox - why should the change in entropy be zero?. The question concerns the following situation: I have some gas of identical particles and they ...
4
votes
3answers
195 views

What is the meaning of Boltzmann definition of Entropy?

I would like to ask if someone knows the physical meaning of Boltzmann's definition of entropy. of course the formula is pretty straightforward $$S=K_b\ln(Ω)$$ but what in the heck is the natural ...
0
votes
1answer
88 views

Entropy and probability

I read "The NEW world of Mr. Tompkins" and I'm not sure with one of the Gamow's equation. When he calculated the probability of entropy, he used this reasoning: "How likely is a situation that all the ...
2
votes
1answer
70 views

Details in the derivation of the second law starting from the phase space volume

I had a question on one of the details of the derivation of the second law of thermodynamics starting from the phase space volume. I'll type out what I understand so far: Letting the Hamiltonian ...
1
vote
1answer
62 views

Calculating energy U from $\partial U/\partial q$

Imagine $N$ oscillators with only two possible energies, $\epsilon_0$ and $ \epsilon_1$, with $\epsilon_1 > \epsilon_0$. Taking $\epsilon_0 = 0$ for now I showed $\Omega(q\epsilon_1) = ...
8
votes
1answer
199 views

Why does $S = k_B \ln W$ not always apply?

I thought for a long time that the Boltzmann formula for entropy, $S = k_B \ln W$, was a universally true statement, or rather the definition of entropy from the perspective of statistical mechanics. ...
4
votes
1answer
211 views

About Boltzmann H-theorem

What is the assumption for Boltzmann H-theorem? One can derive it just from the unitarity of quantum mechanics, so this should be generally true, does it imply a closed system will always thermalize ...
0
votes
1answer
45 views

Maximising entropy when energy is shared between systems

This is a problem to do with statistical physics, and the exchange of energy when we have two microcanonical ensemble. I don't understand why there should be a minus sign in the middle, if Energy* ...
1
vote
1answer
259 views

Boltzmann entropy and phase space volume

In Huang's book on Statistical mechanism and Statistical interpretation of Entropy, it is not mentioned that $\Omega$ is the phase space volume, but it is the states of the system. So, how does ...
2
votes
2answers
137 views

Bolzmann entropy [duplicate]

The Boltzmann entropy is defined as the logarithm of the phase space volume (E). Is there a reference, book, paper which shows where this definition comes and how it is equal to the phase space ...
2
votes
1answer
172 views

Connection between Kolmogorov entropy and Boltzmann entropy

http://math.stackexchange.com/questions/527384/what-is-the-connectivity-between-boltzmanns-entropy-expression-and-shannons-en mentions a relationship between Shannon entropy and Boltzmann entropy. Is ...
0
votes
2answers
161 views

Statistical Entropy and Information theory

I am having trouble in understanding the following concepts : Pg 231 Appendix B of the link ...
2
votes
2answers
57 views

Modeling a list with a tunable degree of disorder/shuffling

Imagine we have a list of ordered numbers $L = (1, 2,\dots, N)$. I want to add an arbitrary amount of "disorder" to that list. For instance: Adding a little bit of disorder would permute a few ...
1
vote
1answer
106 views

What is the probability of ice in boiling water?

Ice crystals are spatially ordered, and in every randomness there is a low possibility of temporarily order. If given enough boiling water, and sufficient time, could local clusters water molecules ...
3
votes
1answer
160 views

Confusions regarding entropy

Help, I am terribly confused about entropy. On the one hand, I am taught at school that a substance such is an ice/solid has a lower entropy than its gaseous equivalent and that a process such as ...
1
vote
1answer
135 views

Can exergy and exergy destruction be understood through thermodynamical and/or statistical-mechanical principles?

My textbook Fundamentals of engineering thermodynamics, Moran and Shapiro states: The exergy is the maximum theoretical work obtainable for an overall system consisting of a system and the ...
0
votes
1answer
61 views

In calculating entropy, why can the partitioning of an ensemble into microstates be chosen “somewhat arbitrarily”?

I'm confused by statistical entropy. It seems to me like the number of microstates for a given macrostate would increase without bound as finer partitionings of the phase space are chosen. Why is it ...
9
votes
1answer
425 views

Motivation for the use of Tsallis entropy

Every now and again I hear something about Tsallis entropy, $$ S_q(\{p_i\}) = \frac{1}{q-1}\left( 1- \sum_i p_i^q \right), \tag{1} $$ and I decided to finally get around to investigating it. I haven't ...
3
votes
3answers
333 views

Entropy increase vs Conservation of information (QM)

Unitarity of quantum mechanics prohibits information destruction. On the other hand, the second law of thermodynamics claims entropy to be increasing. If entropy is to be thought of as a measure of ...
2
votes
3answers
214 views

How does that Boltzmann distribution interact with entropy?

In an ideal gas, the Boltzmann distribution predicts a distribution of particle energies $E_i$ proportional to $ge^{-E_i/k_bT}$. But, doesn't entropy dictate that the system will always progress ...
1
vote
3answers
299 views

Is there really such a thing as an irreversible process?

If an isolated system goes from a state A to B, will it always eventually fluctuate back to state A? If not, give an simple example. Is it right to say that entropy only says that the probability ...
1
vote
2answers
397 views

Why doesnt this violate 2nd law of thermodynamics?

Consider an ideal gas in a cylindrical container in a gravitational field, with a piston on top pushing down by gravity. The piston has some locking mechanism that locks it in place if it is displaced ...
7
votes
1answer
340 views

``What is life?'' by a physicist definition [closed]

The question is about defining ``What is life?'' in the field of Physics. Whether there is any (insightful) way of defining ``What is life?'' from physicists. There are pioneer works, including ...
15
votes
5answers
1k views

Why isn't absolute $0 K$ temperature possible?

So $T$ is defined as $$T = \left(\frac{\partial E}{\partial S}\right)$$ and $S$ is defined as $$S = k_B \ln \Omega$$ where $\Omega$ is the number of accessible states of the system for a given ...
9
votes
5answers
621 views

How do you prove the second law of thermodynamics from statistical mechanics?

How do you prove the second law of thermodynamics from statistical mechanics? To prove entropy will only increase with time? How to prove? Please guide.
2
votes
1answer
338 views

Equation of state of a rubber band

I have the following question that I attached in png format. I have done part (a), but I am having difficulties in part (b) when I proceed according to the book. I have non zero tension at ...
4
votes
4answers
455 views

Entropy as an arrow of time

From what I understand, entropy is a concept defined by the experimentalist due to his ignorance of the exact microstate of a system. To say the number of accessible microstates $W$ of the universe is ...
7
votes
2answers
216 views

Casimir effect as an entropic force

When I first learned about the depletion interaction, my initial reaction was that it looks very similar to the Casimir effect. On making this remark to the professor, he replied somewhat mystically: ...
0
votes
1answer
369 views

Calculating the ideal mixing entropy using Gibbs' entropy formula

Two distinguishable gases are in separate volumes $xV$ and $(1-x)V$ $(x\in [0,1])$ respectively, and the number of particles on each side is $xN$ and $(1-x)N$ respectively. The volumes are separated ...
3
votes
1answer
223 views

Should entropy have units and temperature in terms of energy? [duplicate]

I've been thinking about entropy for a while and why it is a confusing concept and many references are filled with varying descriptions of something that is a statistical probability (arrows of time, ...
4
votes
2answers
338 views

The statistical nature of the 2nd Law of Thermodynamics

Ok, so entropy increases... This is supposed to be an absolute statement about entropy. But then someone imagines a box with a 10 particle gas, and finds that every now and then all particles are in ...
0
votes
0answers
42 views

What is Verlinde's statistical description of gravity as an entropic force? [duplicate]

What is Verlinde's statistical description of gravity as an entropic force leads to the correct inverse square distance law of attraction between classical bodies?
1
vote
1answer
278 views

Why do humans like to break the second law of thermodynamics? [closed]

Roughly speaking, Entropy is a measure of the disorder of a system. However as humans, we tend to do the complete opposite. For instance, in a home if a painting that is hanging on the wall is ...