The study of large systems through coarse graining microscopic descriptions, providing a more detailed understanding of thermodynamics.

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3answers
124 views

Entropy change in an irreversible process between 2 equilibrium state

Calculating entropy change in an irreversible process between 2 states requires computing the change in entropy for any reversible process between the 2 same states, but why? If someone could provide ...
25
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8answers
2k views

How is $\frac{dQ}{T}$ measure of randomness of system?

I am studying entropy and its hard for me to catch up what exactly is entropy. Many articles and books write that entropy is the measure of randomness or disorder of the system. They say when a gas ...
4
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2answers
290 views

What's the most fundamental definition of temperature?

What's the most fundamental definition of temperature? Is it the definition concern about average energy, number of micro states, or what? By "fundamental", I mean "to be applied" in such general ...
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3answers
199 views

Dimensionless entropy interpretation

Measuring temperature in joules instead in the artificial units of Kelvin would render entropy as a dimensionless quantity. This is quite appealing since entropy has always been quite a misterious ...
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1answer
118 views

What is the cause for mechanical equilibrium in statistical mechanics?

In classical thermodynamics, mechanical equilibrium is defined as the state of a system in which there is no net flow of volume as there should be no net pressure within the system. Ok. ...
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0answers
28 views

Speed of electrons at given temperature in non Hydrogen-like atoms

I may be somewhat confused on the topic, so please excuse me if this is really basic. For the Hydrogen atom, one can easily derive the expectation value of the electron's speed: $$ \langle v \rangle ...
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4answers
171 views
+50

How is Liouville's theorem compatible with the Second Law?

The second law says that entropy can only increase, and entropy is proportional to phase space volume. But Liouville's theorem says that phase space volume is constant. Taken naively, this seems to ...
2
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2answers
158 views

Laplace transform of partition function a general result or a mathematical result?

In the following derivation I am trying to show that the function $Z_C(\beta)$ is obtained from the function $Z_M(E)$ by Laplace transform. Let, \begin{equation} \frac{1}{Z_M}\frac{\partial ...
2
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1answer
183 views

Thermal radiation in the Unruh Effect

The following formula has been given in 't Hooft's black holes notes ($|\Omega \rangle$ is the vacuum state of Minkowski space, O is a operator): $$\langle \Omega| O|\Omega \rangle = \sum_{n \ge 0} ...
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1answer
110 views
+50

Dr. Pierre-Marie Robitaille: On the Validity of Kirchhoff's Law

Lately I've been researching about the black-body spectrum and the historical development of Planck's Law. I mainly wanted to understand a little bit more why many different objects (Stars, Hot ...
7
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3answers
1k views

Once a quantum partition function is in path integral form, does it contain any operators?

Once a quantum partition function is in path integral form, does it contain any operators? I.e. The quantum partition function is $Z=tr(e^{-\beta H})$ where $H$ is an operator, the Hamiltonian of the ...
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2answers
60 views

Langevin Equation - Stochastic Differential Equation. What are the subtleties?

I am trying to find out the motion of a particle in 3D governed by the Langevin equation, numerically. Anyway, the Langevin equation is given by $$m \ddot{x} = -(6\pi a\nu) \dot{x} + F_b $$ where ...
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2answers
1k views

Physics-based derivation of the formula for entropy

I am looking for a derivation of the formula $$S~=~-\Sigma_ip_i \log (p_i).$$ for entropy, from first principles. I only wish to assume the laws of physics, and without involving concepts in ...
2
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1answer
25 views

Ewald summation without repeating one particle periodically?

I need to perform an Ewald summation for a Brownian Dynamics simulation. In the normal Ewald summation procedure, all particles in the simulation box are periodically repeated in the neighbouring ...
0
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0answers
41 views

What is the physical meaning of a Partition Function in Statistical physics?

In many places in statistical physics we assume the partition function. To me the explanations after partition functions are most of the times clear but always wonder why a partition function and what ...
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1answer
261 views

Virial theorem and the energy in a gas

I clearly am interpreting the Virial Theorem incorrectly, but I don't know how. In dipole gases, the molecules can exhibit five kinetic modes, while they can only experience 2 potential modes. Doesn't ...
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1answer
26 views

What is meant by the expression “Markovian dynamics”

I know what a Markov chain is but what does it mean in physics when I say that I assume Markovian dynamics? For example in Quantum Mechanics, I read that it means that the time evolution can be ...
0
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0answers
51 views

10 Harmonic Oscillators - Probability of finding one in state n=0 [on hold]

Given are 10 harmonic oscillators with a total energy of $E=2h\nu$. Note that the ground states are not included, since the calculations do not need them! e.g. $E_n= \hbar \omega (1/2 + n)\approx ...
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0answers
55 views

Theoretical physics [closed]

Hi every one I am student who has a high interest in the Ising model. Please I have a question and I hope someone can help me
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1answer
42 views

Temperature increase during friction

There is pin made of Asbestos and two disc material Aluminum and steel in first experiment i used Aluminum disc with asbestos pin in wear test the disc is rotating and the asbestos was in frictional ...
0
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1answer
18 views

The different in wear test when using Aluminum and Steel disc in pin on disc apparatus

In wear test of pin on disc apparatus i found that mass loss of pin when i used Aluminum disc is higher than when i used Steel disc under the same conditions ,pressure, velocity and contact time can ...
3
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1answer
62 views

Is the MaxEnt “interpretation” of statistical mechanics the current mainstream approach?

I've only recently started studying statistical mechanics and I'm quite confused with the MaxEnt and anti-MaxEnt ideas. I'm looking for a concise answer, if it is possible, not really a description ...
5
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1answer
152 views

Phase Transition at Zero Temperature (Not QPT)

As is well known the Ising model exhibits a phase transition, except the one dimensional case in which the phase transition occurs strictly at $T=0$. Now I have always thought that this makes the case ...
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2answers
94 views

Reference for mathematics of statistical mechanics

I'm looking for materials (books, articles, etc) which focus ONLY on the mathematics of statistical mechanics (as I have no background in physics). The materials may have some simple explanations or ...
0
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0answers
27 views

Difficulty in understanding Maxwell Boltzmann distribution in case on ions in a field

I learned that the velocity of molecules obey Maxwell Boltzmann (MB) distribution at a Temperature T. If I have ions of mass 'M' accelerated to 2eV in a specific region. As the ions are not ...
3
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4answers
301 views

Liouville's theorem and the preservation of topology

What might be a simple proof showing that the time evolution of the phase space volume can't lead to splitting off of the phase space volume? By Liouville's theorem, the total phase space volume is ...
2
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1answer
221 views

About the factorial N! in the partition function

After reading these posts: Why is the partition function divided by $(h^{3N} N!)$? , What is the resolution to Gibb's paradox?, and some of these: http://arxiv.org/abs/1012.4111 , ...
3
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1answer
85 views

Local and global detailed balance

I'm taking a course on nonequilibrium statistical mechanics and I encountered the terms local and global detailed balance. I'm a bit confused about what is their exact definition and what is the ...
2
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1answer
57 views

Is the $\mu VE$ ensemble possible to formulate?

I have recently learned about ensembles in statistical mechanics, and I've seen multiple applications and interpretations of the EVN (microcanonical), TVN (canonical), $\mu$VT (grand canonical) and ...
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1answer
34 views

Expected value of an operator in the microcanonical ensemble

I am following professor David Tong's lecture notes on Statistical Mechanics and on page 9 of this file http://www.damtp.cam.ac.uk/user/tong/statphys/one.pdf he states that the expected value of an ...
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0answers
14 views

What is the relation between scattering amplitudes, fluctuations, response functions and correlations in macroscopic equilibrium systems?

In Kardar's book Statistical Physics of Fields, he mentions that that correlations at different length scales can be measured by scattering. If its electric correlations, you would scatter light and ...
0
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0answers
14 views

Is there a way to get the Bethe Roots, that belong to a given eigenvalue of the transfer matrix?

(Quantum) integrable systems, that belong to solutions to the Yang-Baxter-equation, are often solved by the (algebraic) Bethe Ansatz. Solutions to the Bethe-equations lead to the eigenvalues of the ...
0
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1answer
58 views

Why is the correlation of an observable and its derivative zero?

Why is the correlation of an observable and it's derivative zero? And why does this not only hold for $\langle A(t) \dot A(t) \rangle $ but also for $\langle A(0) \dot A(t) \rangle $ ? These averages ...
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3answers
37 views

How to conserve energy with electrical noise?

If a resistor experiences thermal noise, it will dissipate energy to the environment. But where does the resistor's energy come from? It seems that it will just lose energy until ran out.
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2answers
426 views

Definition of stress at the microscale

Take, for simplicity, a Lennard-Jones fluid below the critical temperature, which is to say that there is a phase separation into fluid and gas and thus an interface is formed. The macroscale picture ...
2
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1answer
67 views

The Liouville equation and the BBGKY hierarchy.

The Liouville equation of motion is written in terms of an $N$ particle distribution $f_N$. \begin{equation} \frac{\partial f_N}{\partial t}=\{H,f_N\} \end{equation} Where $\{\cdot ,\cdot \}$ is the ...
3
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0answers
85 views

Why does decay of correlations imply absence of order?

In a few articles I have read, a two-point correlation function $\langle g(x)g(y) \rangle$ is shown to decay with increasing distance of $x$ and $y$, and this is then taken to imply an absence of the ...
2
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1answer
147 views

Reaction coordinate as a function of atomic positions

I'm going over some (molecular dynamics) related literature - specifically the derivation of the Weighted Histogram Analysis Method (WHAM). As a quick backdrop WHAM is a method for stitching ...
0
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0answers
25 views

Books that cover Mode-Coupling Theory

I am looking for a book that covers the schematic mode-coupling theory and that are not too arcane (i.e., recent book). Basically the only book so far on this I have come across is "nonequilibrium ...
2
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0answers
40 views

Classical Statistical thermodynamics phase space and residue $h$

In classical statistical mechanics we have to divide the partition function by a factor of $1/h^n$. In almost every calculation of a real quantity this cancels out and is thought to be a remnant of ...
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0answers
37 views

Is there a local canonical ensemble partition function for a Bose-Einstein gas?

The grand canonical partition function for a Bose-Einstein gas is $$ Z_{\text{grand bos}} = \exp \left( \sum_{j=0}^{\infty} -\ln \left( 1-e^{\beta(\mu-\epsilon_j)} \right)g_j \right) $$ where $\beta$ ...
6
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2answers
219 views

How does statistical mechanics predict that hot air rises?

Does hot air rise -- from a statistical-mechanical viewpoint Question #6329 asks whether and why hot air rises. The consensus answer is straightforward: - hot air is less dense than cold air - ...
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2answers
642 views

How does temperature relate to the kinetic energy of molecules?

In ideal gas model, temperature is the measure of average kinetic energy of the gas molecules. If by some means the gas particles are accelerated to a very high speed in one direction, KE certainly ...
7
votes
3answers
3k views

What are the six degrees of freedom of the atoms in a solid?

A monoatomic ideal gas has heat capacity $C_v=1.5$ which comes from the three translational degrees of freedom. For solids at high temperature, $C_v=3$, implying six degrees of freedom. What are ...
8
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4answers
250 views

Why is the partition function divided by $(h^{3N} N!)$?

When computing partition functions for classical systems with $N$ particles with a given Hamiltonian $H$ I've seen some places writing it as $$Z = \dfrac{1}{h^{3N} N!}\int e^{-\beta H(p,q)}dpdq$$ ...
4
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2answers
216 views

Counting Problems in Physics

What are some classic counting problems in physics? I'm trying to think of interesting examples to give in a math class on the matter, and I feel as if physics should have some ones to offer.
2
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2answers
44 views

Multiplicity vs Partition function

I'm a little confused between all the different notations for the multiplicity and partition function. They're not the same thing, are they? I know that entropy can be expressed as $ S = k \ln\Omega ...
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0answers
28 views

about Conservation laws and Correlation function

I'm reading a review paper by Gorden Baym-(http://www.worldscientific.com/doi/abs/10.1142/9789812793812_0002) In the second part, he raised that: According to conservation law $\frac{\partial ...
5
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2answers
149 views

Simple estimation of the critical temperature of water

I'm trying to develop fermi estimation skills and I came up with a question for which I don't even know where to start from. Here goes: Is it possible to estimate the critical temperature (say in ...
0
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1answer
33 views

Fermi energy on a “fermion pre-gas model”

I'm having serious trouble while trying to follow an example from Callen's "Thermodynamics and an introduction to Thermostatistics" regarding the definition of the Fermi energy. In said example one ...