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

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Hindered rotation model for flexible polymers: deriving the Flory characteristic ratio

In the hindered rotation model we assumes constant bond angles $\theta$ and lengths $\ell$, with torsion angles between adjacent monomers being hindered by a potential $U(\phi_i)$. In Rubinstein's ...
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30 views

A micro-reversible stochastic process that models transitions between states with variable energies

Suppose we have a system with 3 possible states A, B and C (there could be $n$ states as well) with energies $E_a(t)$, $E_b(t)$ and $E_c(t)$ that vary with time. If our system has a constant finite ...
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1answer
56 views

Why is the average thermal velocity 0?

Thermal velocity is the velocity of the free electron due to their random motion. So how is the average value 0?
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1answer
29 views

Example of a Carnot machine made of a different physical system than a ideal gas?

Anybody knows an example of a Carnot machine made with any different thing than a gas? For example wire or a magnet. I was wondering that since I read the Kardar's book on Statistical Mechanics. He ...
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1answer
40 views

What is the difference between these two expressions for the partition function, Z?

What is the difference between these two expressions given for the partition function, Z? $$Z = \sum_{i}e^{-\varepsilon_i/kT}$$ $$Z = \sum_{j} g_je^{-\varepsilon_j/kT}$$ where each energy level has ...
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21 views

Triangular and Kagome lattice anti ferromagnet at zero temperature

The triangular lattice with anti ferromagnetically coupled nearest neighbour ising spins has a power law ordered zero temperature state at the three sublattice wavevector. Kagome lattice, with the ...
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17 views

Fermi-Pasta-Ulam for the beam equation

The Fermi-Pasta-Ulam numerical experiment is based upon the discrete wave equation, with a small non-linearity added to the forcing term. Does anybody know of similar research performed on the beam ...
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6answers
6k views

Why does a system try to minimize its total energy?

Why does a system like to minimize its total energy? For example, the total energy of a $H_2$ molecule is smaller than the that of two two isolated hydrogen atoms and that is why two $H$ atoms tries ...
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1answer
75 views

Poincare recurrence time of the Universe

I've read around a bit, and it seems to be universal that the notion of a Poincare recurrence time for the universe exists. And it seems to be debated that the universe can be given an entropy, as it ...
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4answers
110 views

Is it possible for a system to become irreversible?

Imagine a ball bouncing in a box for a long time. We know, there is a certain path it can go to bounce off infinitely (see the image). If it gets to this state, it will never be able to get back again....
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74 views

Time Scales Of Processes In Molecular Dynamics

Suppose I run a molecular dynamics simulation of a fluid sandwiched between solid walls which are periodic in the lateral directions and finite in the direction of the fluid film thickness. Now, I ...
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1answer
90 views

boltzmann weight factor and statistical ensembles

i am working on a project about in-equivalence between statistical ensembles ( micro-canonical and canonical to be more precise ). how can we show that the in the canonical ensemble the system is ...
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19 views

How to show a ratio of probabilities in Boltzmann statistics from entropy?

Consider a system in a state $s$ of energy $E(s)$ in thermal equilibrium with a reservoir of energy $U_R$, volume $V_R$ and number of particles $N_R$. The ratio of probabilities of being in states $...
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3answers
38 views

Why only $x$-component of gas particle changes when it strikes with wall perpendicular to $x$-axis elastically?

In my book ''Ncert Class 12" It is written We begin by considering the collision of one molecule with one of the walls of the container, oriented with a unit normal vector pointing out of the ...
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1answer
26 views

Statiscal treatment of multiparticle system (Thermodynamics) [closed]

If a system of two energy levels with energies $\epsilon_1$ and $\epsilon_2$ is populated N particles at temperature T. The degeneracy of both levels is one. The particles populate the microstates to ...
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0answers
28 views

Susceptibility at a first-order phase transition

I have two questions about first-order phase transitions: 1) is the susceptibility divergent at a first-order phase transition? 2) if yes, does it diverge in a universal way as in continuous phase ...
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0answers
30 views

Functional Gaussian Integral Involving Gradient Square with non-trivial Kernel

I have been trying to solve the following functional gaussian integral. I've had problem finding the inverse kernel. $f(x)$ and $\rho(x)$ are two known scalar fields and they do vanish at infinity. $...
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3answers
135 views

Does entropy always increase with temperature? [duplicate]

For any system can we always say that entropy increases with temperature. In other words: $$\left(\frac{\partial S}{\partial T} \right)_{\{\alpha\}}\ge0$$ where $\{\alpha\}$ is the set of parameters ...
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1answer
24 views

Why do we have this difference in the multiplicity of Cartesian space and momentum space for a gas?

For an ideal gas, the multiplicity of an ideal gas with $N$ molecules in Cartesian space is $$\Omega_{\text{space}}=\Big(\frac{V}{(\Delta x)^3}\Big)^N.$$ This is pretty intuitive, because we are ...
5
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1answer
133 views

Obtaining the temperature from Bose-Einstein and Fermi-Dirac distribution

Lets say you are given a distribution function $f(p)$ and you want to define a temperature, $T_f$, for this distribution. (I assume $\mu = 0$.) It is then natural to define a temperature the ...
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1answer
78 views

Is there anything comparable to many-body localization in classical physics?

I've only just started looking into many-body localization, so this question may come off as a little vague. But my understanding is that it relates to how some quantum systems do not thermalize, as ...
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2answers
83 views

The calculation of the entropy of a single atom

I used to think that the entropy of a single atom could not be calculated, for in my mind only the entropy of a system containing many atoms could be calculated. But my professor told me the entropy ...
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1answer
66 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
98 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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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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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
75 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
70 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
59 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
24 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
29 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
88 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 ...
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26 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. ...
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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. ...
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1answer
42 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 ...
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1answer
55 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
48 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 ...
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3answers
124 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
31 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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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
43 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 ...
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0answers
107 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 ...
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1answer
75 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 ...
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1answer
62 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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21 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
42 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 ...