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

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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
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 ...
2
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1answer
69 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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42 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
136 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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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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48 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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96 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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42 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
396 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 ...
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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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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
39 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
40 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
64 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
32 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 ...
-1
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1answer
62 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
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1answer
139 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 $...
1
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1answer
79 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 ...
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45 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. ...
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14 views

Counting the accesible microestates compatible with the macrostate conditions

Let be a system consisting of $N$ magnetic dipoles with magnetic dipole $\vec{\mu}$ in a magnetic field $\vec{B}$. I want to count the micro states accessible to the macro estate defined by $E=-\mu B$ ...
0
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1answer
53 views

What happens to Boson and Fermi gases at very low temperature?

At low temperatures Fermi gases pile up to the state with the Fermi-energy having one particle in each state and Boson gases form Bose-Einstein condensates. However, the only derivations I have seen ...
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0answers
22 views

Phase diagram binary mixture

The Gibbs Phase Rule states: F = C - P + 2. From this it is possible to construct a phase diagram. In case of a 1-component system C=1 and where P denotes the number of phases in equilibrium. In case ...
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43 views

Violations of Onsager reciprocity?

As far as I understand it, the modern statement of Onsager reciprocity is that the linear-response transport coefficient matrix, when transposed, is equal to that of the time-reversed system (reversed ...
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1answer
37 views

Physical reason why Prandtl number is order unity for gases?

Is there a physical reason behind the fact that for gases the thermal diffusivity is on the same order of magnitude as kinematic viscosity (and as such a Prandtl number of order unity) and if so what ...
0
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1answer
53 views

Conceptual problem on Maxwell's velocity distribution law

I already read about Maxwell's velocity distribution law for gas molecule. And the expression for that distribution is following dnc=4πnA^3e^(-bc^2)c^2dc Now if we assume that the molecules have no ...
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1answer
51 views

Statistical Mechanics: Computing a system's microstate multiplicity

I have a general question concerning how to compute the microstate multiplicity of a system, in my lecture notes, for a system of $N$ weakly coupled oscillator and $Q$ energy quantas, the multiplicity ...
2
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1answer
53 views

Why does this formula for the partition function not include the multiplicity?

I am having problems understanding the formulas used for describing the partition functions and the probability distributions for canonical ensembles. In the first case I have two formulas for the ...
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0answers
28 views

Linear thermal expansion from statistical mechanics?

I came across a question recently regarding work done by an expanding metal and the origin of the energy used for the work, and most of the responses pointed the person to look more at the enthalpy ...
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0answers
29 views

Microscopic Definition of Heat and Work

If I am given a statistical System, then I can define state-variables like Energy, Entropy or other Observables, and then I can (at least for equilibrium states) give the Change of Energy as: \begin{...
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0answers
20 views

Constancy of Coefficients of Additive Integrals Throughout Subsystems of a Closed System

I'm studying Landau and Lifshitz's Statistical Physics, Part 1, 3rd edition and am looking for clarification on the following statement, which appears on page 11 in the section on The Significance of ...
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0answers
35 views

probability of striking the circular ring by gas molecules

In kinetic theory we use probabilistic case to derive pressure, no. Of molecules having speed c to c+dc or in such cases.and to derive such equations we introduce a term called "SOLID ANGLE" I come ...
3
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1answer
56 views

Quantum versus classical computation of the density of states

If I consider for instance N non interacting particles in a box, I can compute the energy spectrum quantum mechanically, and thus the number of (quantum) microstates corresponding to a total energy ...
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1answer
47 views

Mean free path in QFT

I'm trying to understand the hydrodynamic approximation of a general QFT when the large $k$ and $\omega$ DOF have been integrated out i.e that at highly enough temperature every non-trivial QFT ...
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0answers
13 views

How the degrees of freedom for gas molecules affect energy

It seems a bit unclear to me how degrees of freedom help judge the amount of kinetics energy in the system. from the formula for the energy of molecule ε = u0 + (v/2)kT it can be inferred that the ...
10
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1answer
956 views

What leads to the existence of critical temperature?

We know that $T_c$ is the temperature above which no amount of pressure could force a gas to liquefy. But why is this? Somehow I don't buy the point that the gas molecules exert too much pressure ...
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1answer
49 views

How to write any partition function?

So I am familiar with the derivation of the partition function for a canonical and a grand canonical ensemble. I have seen definitions of the partition function for some of the quantum counterparts of ...
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1answer
41 views

water stream cut off abruptly; why there will occur sprinkling?

Suppose that water flows with constant velocity $V$ and constant pressure $p$ through a pipe with diameter $d$. Now the pipe is suddenly cut such that the water will splash out of the pipe into the ...
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0answers
31 views

How to derive latent heat from the degrees of freedom in an equation [closed]

I am having some trouble solving a question on statistical mechanics, any help? Q: A certain material vaporizes from the liquid phase at 700 K. In both phases, the molecules have three degrees of ...
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0answers
32 views

Confusion about the number of micro states and approximating it for large number of particles

Hopefully after reading the meta site, I can now rephrase the question as more relevant to this site, this is a question related to statistical physics: Let us suppose we are given a system with $...
5
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1answer
88 views

Ultraviolet catastrophe in a classical world

In the real world, the ultraviolet catastrophe doesn't happen because the quantization of photons modifies the classical behavior of light at frequencies comparable to and higher than the temperature. ...
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40 views

Ising model as quantum model?

I've read in a few papers things that use the fact that the $2D$ Ising model can be interpreted as a $1+1$ quantum spin model. I haven't been able to find this description and would like to read about ...
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63 views

Second law of thermodynamics in linear response theory

I am wondering about the appearance of irreversibility in the response functions or equivalently the correlation functions in a statistical mechanics system. The main principle that I have seen where ...
8
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2answers
255 views

Itô or Stratonovich calculus: which one is more relevant from the point of view of physics?

Langevin equation provides an example of a physical model which involves a differential equation with a stochastic term. Now, I wonder, how should one treat this? When I studied stochastic processes, ...
2
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1answer
64 views

Physics of tagging at B factories

At some B factories, mesons carrying $b/\bar{b}$ quarks are created by $e^-e^+$ collisions at $\gamma(4S)$ resonance. $\gamma(4S)$ decays into antisymmetric wavefunction given by $$ \frac{1}{\sqrt{2}}...