3
votes
1answer
90 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
134 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
66 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
60 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
59 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
184 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
139 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
37 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* ...
0
votes
1answer
167 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
116 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
123 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
125 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
44 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
96 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
139 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
106 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
57 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
239 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
235 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
187 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
votes
3answers
282 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 ...
0
votes
2answers
367 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 ...
6
votes
1answer
280 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 ...
8
votes
5answers
463 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
253 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
409 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
193 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
295 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
185 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
277 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
199 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 ...
1
vote
1answer
93 views

Explanation Needed: Thermodynamics of a hot/cold water jet machine

I didn't know where to begin with this problem. I eventually found a solution online, which is why I'm reposting this question with an answer. I was wondering if anyone can explain the one question I ...
6
votes
1answer
955 views

Clear up confusion about the meaning of entropy

So I though, and was told, that entropy is the amount of disorder in a system. Specifically the example of heat flow and it flows to maximize entropy. To me this seemed odd. This seemed more ordered ...
1
vote
1answer
717 views

Sackur-Tetrode equation - clarification required - problem with units

I'm a 2nd year physics undergraduate and recently I've volunteered to give a short presentation on the Sackur-Tetrode equation derivation and its use at removing the Gibbs paradox. I've looked on the ...
7
votes
4answers
513 views

Definition of the entropy

In physics, the word entropy has important physical implications as the amount of "disorder" of a system. In mathematics, a more abstract definition is used. The (Shannon) entropy of a variable $X$ is ...
4
votes
5answers
374 views

If particles can find themselves spontaneously arranged, isn't entropy actually decreasing? [duplicate]

Take a box of gas particles. At $t = 0$, the distribution of particles is homogeneous. There is a small probability that at $t = 1$, all particles go to the left side of the box. In this case, entropy ...
1
vote
3answers
331 views

Mathematical proof of non-negative change of entropy $\Delta S\geq0$

I understand that we can prove that for any process that occurs in an isolated and closed system it must hold that $$\Delta S\geq0$$ via Clausius' theorem. My question is, how can I prove this in a ...
1
vote
1answer
180 views

Calculating the change in entropy in a melting process

I have a homework question that I'm completely stumped on and need help solving it. I have a $50\, \mathrm{g}$ ice cube at $-15\, \mathrm{C}$ that is in a container of $200\, \mathrm{g}$ of water at ...
1
vote
1answer
167 views

Basic energy calculation for N identical spin system

We have a system that has N identical spins $n_i$, and each spin can be in state 1 or 0. The overall energy for the system is $\epsilon\sum_{i=1}^{N}n_i$. My understanding: There is only one ...
0
votes
1answer
121 views

Uncertainty and Thermodynamics

Dilemma The uncertainty principle of energy and the 2nd law of thermodynamics don't add up : the uncertainty principle of energy says that $\Delta \tau \cdot \Delta E \ge \frac{h}{4\pi} = ...
4
votes
3answers
494 views

Does entropy really always increase (or stay the same)? [duplicate]

Consider this image. If the big (grey) molecules were all to spontaneously move to the left, and the small ones were to move to the right, there would be an increase in order. While unlikely, ...
4
votes
3answers
417 views

Is there a mechanism for time symmetry breaking?

Excluding Thermodynamic's arrow of time, all mathematical descriptions of time are symmetric. We know the arrow of time is real and we know the equations describing physics are real so is there any ...
2
votes
1answer
115 views

How can dQ/T be interpreted as a system's level of disorder?

Long before statistical mechanics, entropy was introduced as: $dS = \frac{dQ}{T}$ At the time when entropy was introduced in this manner, was it known that entropy represents how "disordered" a ...
14
votes
4answers
343 views

Comments on entropy and the direction of time in Landau and Lifshitz's Statistical Mechanics

In Landau and Lifshitz's Stat Mech Volume I is the comment: However, despite this symmetry, quantum mechanics does in fact involve an important non-equivalence of the two directions of time. ...
0
votes
2answers
211 views

How to compute configurations (entropy) of a system?

If we have a system $X$ consisting of subsystems $X_1$ and $X_2$. We also know that $X_1$ and $X_2$ have eigenstates $H_1 = 1 \times 10^{20}$ and $H_2 = 1 \times 10 ^{22}$. Can we calculate the ...
1
vote
1answer
241 views

relation between first law of thermodynamics and statistical mechanics definition of entropy

From the definition of entropy as $S= - Tr (\rho\, ln \rho)$ one obtains that $S = \frac{\langle E \rangle}{T} + \log Z.$ The first law of thermodynamics has $dS = {dE \over T}$. Why is there no ...
4
votes
1answer
318 views

Why is (von Neumann) entropy maximized for an ensemble in thermal equilibrium?

Consider a quantum system in thermal equilibrium with a heat bath. In determining the density operator of the system, the usual procedure is to maximize the von Neumann entropy subject to the ...
4
votes
5answers
4k views

For an isolated system, can the entropy decrease or increase?

In any sizable system, the number of equilibrium states are much, much greater then the number of non-equilibrium states. Since each accessible micro state is equally probably, it is overwhelmingly ...