8
votes
1answer
74 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
0answers
94 views

Quantum entaglement and the arrow of time

I have seen several claims to that quantum mechanics is required to explain the arrow of time which I take to mean the macroscopic irreversibility of physical systems. This is presumably to resolve ...
1
vote
0answers
37 views

Chemical potential of photons

Why do photons have zero chemical potential and what is its the physical significance? From what I know the chemical potential could be interpreted as the energy per unit particle that is put into a ...
2
votes
1answer
72 views

Thermodynamics, chaperones : How to model polymer fragmentation

Living polymers are well described by equilibrium statistical physics. Now I would like to consider a case were living polymers undergo fragmentation due to chaperones. I can think of a kinetic ...
2
votes
1answer
82 views

Quantum Fourier Transform and Entropy

QFT is a nonlocal unitary transformation and so can generate entanglement in a system. It means a separable pure state can be converted into an entangled pure state. Now since the presence of ...
0
votes
2answers
37 views

Is there an analogue to the role of vapor in liquids and gases, but for solids and liquids?

It seems common for an ordered phase to have some amount of disorder present. For example, the average moment of a ferromagnet is less than maximum except at T=0 due to the presence of fluctuations. ...
4
votes
1answer
74 views

A real gas with gravitation-like interaction

Consider a system (a gas) of point-like particles with a gravitation-like interaction (potential) $V(r) \sim \frac{1}{r}$ between pairs of them. One can rule out statistically that two particles will ...
8
votes
5answers
100 views

How can point-like particles in an ideal gas reach thermodynamical equilibrium?

Having learned that the particles of an ideal gas must be point-like (for the gas to be ideal) I wonder how they can reach thermodynamical equilibrium (by "partially" exchanging momentum and energy). ...
0
votes
0answers
19 views

What is Fermi energy and Fermi level? [duplicate]

What is meant by Fermi level and Fermi energy? And what is the difference between the two?
4
votes
0answers
73 views

Nonequilibrium thermodynamics in a Boltzmann picture

The Boltzman approach to statistical mechanics explains the fact that systems equilibriate by the idea that the equillibrium macrostate is associated with an overwhelming number of microstates, so ...
8
votes
3answers
595 views

Why must the particles of an ideal gas be point-like?

Why is a gas of elastically colliding hard balls of finite size not ideal? Respectively: Why is it essential that the particles of an ideal gas are point-like? Especially: Which ...
1
vote
2answers
61 views

System in mechanical but not thermal equilibrium

Let's say there are two systems which can interact by a moving wall but cannot exchange heat. Then the system will be in mechanical, but not necessarily in thermal equilibrium. The maximality of ...
3
votes
2answers
83 views

Why is the Gibbs Free Energy $F-HM$?

With magnetism, the Gibbs Free Energy is $F-HM$, where $F$ is the Helmholtz Free Energy, $H$ is the auxiliary magnetic field, and $M$ is magnetization. Why is this? Normally, in thermodynamics, we ...
2
votes
1answer
62 views

Lennard-Jones induced pseudo-molecules

It can be shown that the Lennard-Jones potential - which describes the interaction between particles in non-ideal gases - gives rise to pseudo-molecules: after a triple "collision" of three ...
3
votes
2answers
363 views

Physical significance of negative temperature

I read some answers regarding negative temperatures but I think my question is new. I want to know that what is the physical significance of negative temperature. Suppose I say a body has ...
1
vote
1answer
65 views

Understanding collision terms in Boltzmann equation

I am reading a paper that deals with the Boltzmann equation. They add a collision which is supposed to account for collisions which happen when particles are within a radius of $d$ from each other. ...
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 ...
0
votes
1answer
64 views

How do we know that the Virial Expansion exists?

How do we know that the Virial Expansion exists? How do we know that we may always write $\frac{p}{kT}$ as a power series in $\frac{N}{V}$? That is, how do we know that there exists $B_{i}$ so that ...
0
votes
1answer
62 views

Why is $B(T)\approx b(T-T_C)$ near critical point $T_C$ in Landau theory?

In Peskin&Schroeder page $270$ equation $(8.4)$ you see that they approximate the function $B(T)$ near the Curie temperature as $$B(T)\approx b(T-T_C)$$ i.e. they omit $B(T_C)$ in the Taylor ...
0
votes
1answer
48 views

Law of equipartition

Law of equipartition predicts the heat capacity of gases correctly. It assumes that inter-molecular attraction in gases is negligible (which is true). But for solids, inter-molecular attraction is not ...
2
votes
5answers
286 views

Does it take infinite energy to create a perfect vacuum?

Question is inspired by a recent burst of perpetuum mobile-type questions. It would be nice if one could simply discard them all by an argument that shows it's impossible to create a perfect vacuum. ...
1
vote
2answers
46 views

Temperature limit on entropy of a paramagnet

We have $$S=Nk_B[\ln(2 \cosh(x)) - x \tanh(x)]$$ where $$x = \frac{\mu B}{k_BT}$$ In need to show that at low temperatures entropy $$S \approx Nk_B2xe^{-2x}$$ I wrote out the $\cosh(x)$ in terms of ...
0
votes
2answers
80 views

On the distinction of past and future: could one theoretically reverse direction of particles and cause time to appear to go backwards?

Based on my understanding of physics after seeing The Distinction of Past and Future on Project Tuva, there is no distinction between past and future on a fundamental level- all particle interactions ...
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 ...
0
votes
2answers
74 views

Entropy of a chain

A chain has N segments which can be oriented in either the x or y directions. For each segment oriented along y, there is an energy penalty of $\epsilon$. We also know the end segment is at $(L_x, ...
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) = ...
4
votes
3answers
123 views

When to use the Boltzmann distribution and the chemical potential?

How do you know when to use the Boltzmann distribution for a particular problem? I have many polymers connected together in many different possibilities by connector agents. All are in a solvent. I ...
0
votes
0answers
33 views

Spin version of Maxwell's demon: Where's the energy?

I have confused myself about the following variant of Maxwell's demon and I can't seem to find out where the energy went. Consider this: You have a chain (one dimension) of spins (up/down) with a ...
1
vote
0answers
37 views

What is the difference between thermodynamical equilibrium and statistical equilibrium?

I am trying to understand what is the different between thermodynamical equilibrium and statistical equilibrium, for example, between photons and electrons at the early universe. (I read through paper ...
7
votes
3answers
217 views

Temperature; Why A Fundamental Quantity?

Temperature is just an indication of the combined property of mass of the molecules and their random motion. We can explain no effective energy transfer between two conducting solid bodies in contact ...
-1
votes
1answer
61 views

Relation between a Quasistatic and a reversible process

Why is it that if a process is reversible, it is quasi-static? Does it mean that then the process is also non-dissipative if it is quasistatic?
0
votes
0answers
165 views

Ultra-Relativistic Fermi Gas - Chemical Potential and Energy

I tried deriving the expression for chemical potential of a Relativistic Fermi Gas using asymptotic expansion (for large z) in : $$ N = \frac{V}{h^3}4\pi (KT)^3g_s \int \frac{p^2 dp}{e^{p-\nu}+1} $$ ...
0
votes
1answer
38 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
2answers
167 views

If quantum gas goes below 0K, is calling 0K absolute zero irrelevant?

Lord Kelvin defined the absolute temperature scale in the mid-1800s in such a way that nothing could be colder than absolute zero. Physicists later realized that the absolute temperature of a gas is ...
1
vote
2answers
88 views

General Thermodynamic equation of state

I heard my professor saying that the equation $$ PV = \frac{2}{3}U $$ is valid for any non-relativistic gas, be it Ideal or Real gas(includes quantum ideal gases). Is this true, If it is how can we ...
1
vote
1answer
120 views

Questions about Statistical Mechanics

For grand partition ensemble, is it true that the introduction of chemical potential allows us to have the sum of number of the particles in each state to be the total number of particles ("On ...
0
votes
0answers
28 views

Statistical mechanics prerequisite [duplicate]

I`ll be taking senior level and graduate course in statistical mechanics in a month. I was wondering what would be the best statistics and probability textbook to prepare for it? I`m currently ...
3
votes
1answer
141 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
241 views

Using the Maxwell-Boltzmann distribution function to find specific molecule speeds?

I've been looking for problems to practice on this topic and found a problem asking to use the Maxwell-Boltzmann distribution function to calculate the fraction of Argon gas molecules with a speed of ...
1
vote
1answer
109 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 ...
2
votes
2answers
347 views

Probability of Different States - Canonical Ensemble - Partition Function

Consider a canonical ensemble of $N$ ideal gas atoms, which could have spin up or spin down. Why is it that the probability of finding the particle in a spin up state generally only involves the ...
1
vote
0answers
146 views

Average number of spin up particles

In a paramagnetic system, where $N = N_\uparrow + N_\downarrow$ is fixed, how does one calculate the average number of spin-up particles $\langle N_\uparrow \rangle$? You can assume we have the ...
2
votes
1answer
440 views

Partition Function for Two Level System

I have a system with $N_s$ sites and $N$ particles, such that $N_s >> N >> 1$. If a site has no particle, then there is zero energy associated with that site. The $N$ particles occupy the ...
5
votes
0answers
332 views

Is Feynman talking about the Zeroth Law of Thermodynamics?

In Volume 1 Chapter 39 of the Feynman Lectures on Physics, Feynman derives the ideal gas law from Newton's laws of motion. But then on page 41-1, he puts a caveat to the derivation he has just ...
1
vote
2answers
138 views

Paramagnetism and large N

In a paramagnetic system, we have: $$N = N_\uparrow + N_\downarrow$$. If we have a large system, with $N >> 1$, is it generally okay to assume $N_\uparrow \approx \frac{N}{2}$ and ...
1
vote
3answers
175 views

Distinguishable, Indistinguishable Paramagnetic Ideal Gas

In the canonical ensemble, the partition function for an ideal gas is given by: $$\frac{Z}{N!}$$ The factor $N!$ accounts for the indistinguishability of the particles of the ideal gas. What ...
2
votes
1answer
83 views

Can I express the heat flow of a fluid in terms of estabilshed characteristics of the velocity distribution?

If $\rho$ is the mass density of a fluid and $A({\bf v})$ is an function of the velocity, which is distributed according to $f({\bf v})$, we have an averaging process $A\mapsto \langle A\rangle:=\int ...
9
votes
0answers
181 views

Can Lee-Yang zeros theorem account for triple point phase transition?

Now the prominent Lee-Yang theorem (or Physical Review 87, 410, 1952) has almost bocome standard ingredient of any comprehensive statistical mechanics textbook. If the volume tends to infinity, ...
3
votes
3answers
246 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 ...
4
votes
1answer
449 views

Paramagnetism Spin-1/2 Particles - Partition Function

I'm trying to come up with an expression for the partition function of a system of spin-1/2 ideal gas particles on a line of length $L$. The total number of particles $N$ is fixed, with $N = ...