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

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1answer
63 views

If Black holes are maximal entropy how can they evaporate?

According to Hawking/Bekenstein a black hole represents the highest amount of entropy for a given volume, (actually the entropy is related to the surface area of the black hole but the fact that they ...
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2answers
90 views

Entropy always increases in a closed system - what if the universe is open?

An interesting question I was asked: Entropy always increases in a closed system - what if the universe is open? Does that mean that entropy can decrease in such a system? Of course, I think there is ...
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0answers
16 views

Rugged Energy Landcapes (Free Energy vs Potential Energy Questions)

A spin glass has what is called a "rugged energy landscape." That is, when you cool down below a certain temperature, the system divides into many wells, all corresponding to slightly different ...
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0answers
31 views

How do inverse of Kirchoff matrix of a polymer possess the information for its mobility?

In Normal Mode Analysis of polymers like proteins, I have seen that mobility (measures like root mean squared fluctuations) can be found from the eigen values and eigen vectors of inverse of Kirchoff ...
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1answer
72 views

Operator formalism in QFT in Euclidean space-time

In QFT there are two very useful general approaches to study quantum fields (on the Minkowski space-time): path integrals and operator formalism. Sometimes they give the same results, sometimes one ...
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1answer
67 views

Deriving Ideal Gas law from Hamiltonian Mechanics

I just don't understand the explanation in Wikipedia. Is there a nice & elegant way of arriving at the Ideal Gas Law from Hamilton's Equations?
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3answers
57 views

When does the Boltzmann distribution apply?

What are the requirements for a system to be described by the Boltzmann distribution in equilibrium? For example, should all the particles be identical? No attractors in the phase space? ...
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0answers
22 views

Construct recurrence relation for the temporal evolution of a Master equation

Say that we have a system evolving over discrete timesteps. The quantity we are interested is X and is given by a distribution $P_X$. This distribution is evolving temporally, and we have a ...
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1answer
39 views

Entropy for $N$ number of particles [closed]

If there are $N$ number of non-interacting and distinguishable particles which have either Energy $E_1$ or $E_2$ , then a. What will be the entropy $S(n)$ for such system? ($n$ is the number of ...
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0answers
28 views

Extensiveness of entropy in classical microcanonical ensemble

In introducing microcanonical ensemble of classical statistical mechanics one pretty much starts by postulating that entropy of the system has the form $S(V,E) = k \log \Gamma(V,E)$, where $\Gamma$ ...
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2answers
84 views

A conceptual question related to statistical mechanics

Statistical mechanics allows us to consider an ensemble of systems, each of which consisting of only a single particle. Once we write the partition function for the system of one particle, we can ...
0
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0answers
25 views

Spread of gases in a room

I have had some thermodynamics and statistical mechanics, but I don't know much fluid mechanics. I am not sure how to model the spread of gases in a room in the case of a fire or some leaking vent. ...
4
votes
3answers
58 views

Why do Temperatures Equalize

I have some Oxygen at Temp A in one container and some Nitrogen at Temp B in another container. If I mix these two containers eventually both the Oxygen and Nitrogen will be at the same temperature. ...
0
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1answer
40 views

White noise in the Langevin model and it's autocorrelation function

I am having some trouble understanding and interpreting the noise term in the Langevin equation for a colloidal particle in a fluid. By the Langevin model, I mean the following model as the equation ...
1
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1answer
54 views

Two definitions of the density matrix?

There seems to be two different definitions of definitions of density matrices in Physics. In Quantum Information we define a the density matrix associated with a wave function $ | \psi \rangle$ as $...
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0answers
47 views

Can the second law of thermodynamics be violated in a small enough system if tried repeatedly enough?

Second law of thermodynamics is observed in the universe because statistics favors it, right? And in large enough system this statistical tendency becomes certainty. Does it also mean that negative ...
8
votes
3answers
119 views

Gross “temperature” of a globular cluster

Globular clusters can be very large, which means we can do statistics about the stars in them. And that means we can try matching their star-as-particle potential/kinetic energy distribution against ...
0
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1answer
30 views

Why use dimensionless heat capacity?

Perhaps this is blindly obvious, but in typical discussions of statistical mechanics (with, say, constant volume) one often finds that, rather than using the heat capacity $$ C_V = \frac{\partial E}{\...
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0answers
25 views

How to interpret two distinguishable particles with N possible states?

NOTE: Please do not provide an answer to the questions. If I am incorrect, please explain why, and if I am correct, please try to further my understanding. I think that this is a constructive way to ...
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0answers
42 views

Calculation of charged sphere distribution near a wall in Cartesian coordinates

I am following a similar derivation as found in the beginning of this paper "Quantitative aspects of the growth of (charged) silica spheres" by A.P. Philipse. This paper calculates the growth of a ...
3
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0answers
105 views

Understanding various types of motion

In classical statistical mechanics, given a system of particles, one often goes about classifying various dynamics (or types of motion) the system may exhibit on different time scales, but studying ...
4
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1answer
72 views

A seemingly paradox for Eigenstate Thermalization Hypothesis (ETH)

ETH states that for a system, all of its eigenstates thermalize. To be more specific, consider an energy eigenstate of the full system $H|n\rangle=E_n|n\rangle$. If the full system is in this ...
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0answers
33 views

Is the equipartition theorem derivable from more basic principles [duplicate]

Is the equipartition theorem really a theorem and derivable from more basic assumptions or is it just a hypothesis. Some of the ways energy is partition is not to squared quantum numbers (e.g. ...
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1answer
32 views

What is the word describing the pairs: temperature and energy, chemical potential and particle number?

I keep forgetting the word describing the pairs of coupled quantities in stat. mech. e.g. inverse temperature $\beta$ and internal energy $E$ or chemical potential $\mu$ and particle number $N$. I ...
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0answers
47 views

Connection between statistical and quantum mechanics

I am aware of Gibbs measures, given the energy (Hamiltonian) of an arrangement, one can determine the frequency of the arrangement. Plug the energy level in the Boltzman equation and there you go. I ...
3
votes
1answer
59 views

Is the principle of indifference enough to derive the microcanonical ensemble?

The microcanonical ensemble is usual motivated solely by the principle of indifference. Textbooks usually say something along the lines of "If the only thing we know about a system is its total ...
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0answers
20 views

Gradient effects in continuum mechanics

What I have learned is that inhomogenous materials (materials with different material properties over space and time) can be treated by the homogenization technique (https://en.wikipedia.org/wiki/...
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1answer
41 views

Conservation of energy and realm of possibility

The law of conservation of energy states that energy cannot be created or destroyed. Based on this principle, you can safely conclude that any effect resulting from a cause must somehow keep all ...
2
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1answer
66 views

Hamiltonian or free energy corresponding to 2+1D Kuramoto-Sivashinsky model

I am trying to understand if the deterministic 2+1D Kuramoto-Sivashinsky equation $$ \partial_t h = -\nu \nabla^2 h - K \nabla^4 h + \frac{\lambda}{2} (\nabla h)^2, $$ where $\nu$, $K$, $\lambda$ ...
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0answers
41 views

Intuition on Gibbs measures

I am (roughly) aware of the way Gibbs measures are used to solve physical systems (e.g. the Ising model). We can basically boil it down to pinpointing a Hamiltonian. My question is, consider a ...
3
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1answer
133 views

Why don't we observe spontaneous symmetry restoration in nature?

Why do we always observe spontaneous symmetry breaking in nature and not restoration? Does there exist some argument with the 2nd law of thermodynamics and the entropy of the universe increasing? If ...
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0answers
32 views

Statistical mechanics - average particle energy, average kinetic energy

I'm looking at derivations for average particle energy giving $E=kT$: http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/bolapp.html And average particle kinetic energy giving $K_E=\dfrac{3}{2}kT$: ...
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0answers
47 views

Deriving the correlation function of a system interacting with a bath of harmonic oscillators

I'm working on the book Quantum Effects in Biology by Mohesni et all. My question is however not biology related, it is about a section on quantum master equations in the weak system-bath coupling ...
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0answers
94 views

How to derive equation for time it takes photons to diffuse through the Sun

I am wanting to use the Rosseland radiative heat flux equation to find the time it takes for photons to diffuse through the sun. The answer I am wanting to derive is: $$\tau_D~\frac{\rho \bar C_p R^...
3
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0answers
41 views

Manking sense of an entropy equal $k_B\frac{1}{2}\ln(2)$

In problems of impurities coupled with electrons in a conduction band, like the Kondo model, is common to represent the entropy contributed by the impurity, in terms of bits, i.e. in units of $k_B\ln(...
5
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4answers
389 views

Why is entropy an extensive quantity?

If we have two identical isolated macroscopic systems both with energy $E$. The number of accessible states of each of them is $\Omega(E)$ and hence the entropy is $\ln\Omega(E)$. Now if we put them ...
2
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0answers
39 views

Decimation of a triangular lattice [closed]

Consider the network of spins shown below. The Hamiltonian is given by $$H = - \sum_{\langle i j k \rangle} [J \sigma_i \sigma_j \sigma_k + J_0]$$ with $J,J_o \geq 0$ and $\langle i j k \rangle$ ...
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0answers
31 views

What is melting / boiling from the statistical viewpoint?

Microscopically, solids are usually described as "completely ordered" and "strongly bound", liquids "somewhat ordered", and gases "unbound" and "disordered". Thermodynamics predicts that the ...
4
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0answers
49 views

How can we show that the BBGKY hierarchy is time symmetric?

I am trying to mathematically show that the BBGKY hierarchy for s particles is time symmetric by setting $t\rightarrow -t$. Using the Wikipedia notation for the s-particle we have $\frac{\partial f_s}...
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0answers
38 views

How to deduce the modified Flory-Huggins equation in this form?

In the paper of "Solution Properties of Poly(N-isopropylacrylamide)" (M. Heskins and J. E. Guillet, Journal of Macromolecular Science: Part A - Chemistry, Vol. 2, Issue 8, pages 1441-1455, 1968), they ...
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1answer
37 views

Voltage homogeneity across cell membrane

During respiration, individual cells produce a relatively large potential difference ($\sim 100$ mV) between the inside and outside, using energy to pump $H^+$ out of the cell to the liquid ...
0
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1answer
37 views

Derivation for the most probable macrostate for distinguishable particles using lagrange's method of undetermined multipliers

We have an expression for $\Omega$ (occupation of each macrostate) in terms of $n_i$ (occupation numbers) . We want to find the $n_i$ which maximises $\Omega$. We now that $$ln[\Omega]=ln[N!]-\...
4
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0answers
61 views

Interpreting the Fourier transform of a Gibbs measure

Recall that a Gibbs measure gives a probability distribution on states $x$ of the form $$ p_X(x) = \frac{1}{Z(\beta)}\exp(-\beta E(x)) $$ As I understand, the function $E$ is interpreted as the ...
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0answers
26 views

What does 'fully excited' actually mean?

In statistical mechanics you often hear the phrases such as 'when the degrees of freedom are fully excited then....'. An example would be the validity of the equipartition theorem. But what is the ...
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1answer
61 views

Cross-differentiation to derive the maxwell relation $\left(\frac{\partial T}{\partial V}\right)_S = -\left(\frac{\partial P}{\partial S}\right)_V$ [closed]

How can I use $T=\left(\frac{\partial E}{\partial S}\right)_V$ and $P=-\left(\frac{\partial E}{\partial V}\right)_S$ to derive $$\left(\frac{\partial T}{\partial V}\right)_S = -\left(\frac{\partial ...
3
votes
1answer
118 views

Quantum field theory: zero vs. finite temperature

I have recently been made aware of the concept of thermal field theory, in which the introductory statement for its motivation is that "ordinary" quantum field theory (QFT) is formulated at zero ...
0
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1answer
35 views

Microcanonical ensemble: imanation for $N$ particles

Q: Consider an isolated system of $N$ non-interacting spins or magnetic dipoles with magnetic moment $\vec{\mu}=\mu_{z}\hat{z}$ and spin S=$1$, so we have $m_{z}=(-1,0,1)\hat{z}$, in a magnetic field $...
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1answer
78 views

Statistical Physics: How do we derive this equation?

I'm reading through Statistical Physics by F. Mandl and there is a step in arriving at an equation that I don't follow. He uses $$P = \sum_r p_r \left(-\frac{\mathrm dE_r}{\mathrm dV} \right) \tag{4....
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2answers
37 views

Inverting density in favour of fugacity

In these notes on pages 80 and 81 the following step was used The density in terms of fugacity is $$ \frac{N}{V} = \frac{z}{\lambda^3}\left ( 1+ \frac{z}{2 \sqrt{2}} + \ldots \right ) $$ and this ...
5
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0answers
41 views

Is there any useful sense in which entropy fluctuates?

One of the classic distinctions between young Boltzmann and old Boltzmann was his view on entropy. Young Boltzmann had his H-theorem where a mechanical quantity H was supposed to represent entropy. ...