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

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Definition of Entropy for reversible and irreversible process

$\int \dfrac{\delta Q}{T}$ can't be used to calculate entropy of an irreversible process. If you happen to know heat supplied and temperature at which it is supplied for just an instant. Can you then ...
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12 views

What is the central charge of the $q$-state Potts model, for large $q$?

The central charge of a model, is, heuristically related to the number of microscopic degrees of freedom. Is there a simple argument for the asymptotic behavior of the central charge for the $q$-state ...
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26 views

Efficiency larger than one?

The efficiency of a heat engine is the work we can do divided by the heat we take out of the hot reservoir. This quantity is always $ \le 1$. The efficiency of a heat pump is the heat we can release ...
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38 views

Is Boltzmann distribution contradicting with the fundamental assumption of statistical thermodynamics?

In equilibrium statistical physics the fundamental assumption of statistical thermodynamics states that the occupation of any microstate is equally probable (i.e. $p_i=1/\Omega, S=-k_B\sum p_i\,{\rm ...
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collision rates [on hold]

You have a container with $n_A$ gas molecules of type $A$ and $n_B$ gas molecules of type $B$. Consider bi-molecular collisions. Denote by $C_{XY}$ the total number of collisions of $X$ and $Y$ type ...
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49 views

Why don't we have particles whose wavefunctions are symmetric wrt one exchange operator and anti-symmetric wrt other exchange operator?

Consider a system with $n$ identical particles. Let the wavefunction of the system be $\psi(r_1,\ldots, r_2)$. Let $P_{a,b}$ represent the exchange operator which exchanges particle $a$ with particle ...
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22 views

Physical meaning of RG transformation

When we do RG transformation in Statistical mechanics we eliminate unnecessary degrees of freedom and it leads us to the fixed point. How can I visualize it physically?
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28 views

How to derive the Bhatnagar-Gross-Krook collision integral from Boltzmann one?

Let's have Boltzmann collision integral: $$ I_{coll} =\int d \sigma d^{3}\mathbf p_{1}(ff_{1} - f{'}f{'}_{1})|\mathbf v_{rel}|.\tag{1}\label{1} $$ How to transform $\eqref{1}$ to BGK collision ...
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16 views

Free bosons with an attractive/repulsive defect

Consider a system of non-interacting bosons hopping in a qubic lattice in 2D or 3D. A single site of the lattice is an attractive/repulsive defect. Formally, let $H=-t\sum_{<i,j>}(a_i^\dagger ...
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62 views
+100

Why are large scale structures isotropic in the Ising model?

I have at least a qualitative understanding of why the critical state of the Ising model is scale invariant, by arguments to do with renormalisation, which I understand only very roughly. However, in ...
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30 views

Partial derivative of energy in the grand canonical ensemble

I am struggling with basics in here: I know that $U=U(N,V,T)$ and $z=z(N,V,T)$ so that $N=N(z,V,T)$. Now, I want to do partial differentiation using chain rule involving three variables so that I ...
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27 views

How is energy transferred in Joules law of heating?

Joule's law of heating states that an accelerated electron loses its energy, which is then converted into heat energy, by colliding with vibrating atom i.e ions in their lattice site. but we know atom ...
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37 views

Canonical Distribution (Partition Function)

For the canonical distribution $$ w_{n}=e^{(F-E_{n})/T}, $$ is the sum $$ Z=\sum_{n}e^{E_{n}/T} $$ a sum over energies or a sum over states? Perhaps this is a silly question, but Landau and Lifshitz ...
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56 views

Ising model 2-dimensional - ground state configuration

I have to prove something about the 2-dimensional ising model. The problem is the following: Prove that every nearest-neighbour and next-nearest-neighbour interaction on the square lattice ...
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1answer
27 views

Simulating Phase Space Evolution

I am interested in modeling the time evolution of phase-space $\rho(\vec{q},\vec{p},t)$. I have attempted to use Liouville's theorem $\partial_t\rho=-\sum_{i=1}^{3}(\partial_{q_i}\rho)\dot ...
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19 views

How to find Entropy of system in terms of Magnetic Field and Temperature

I'm studying for final exams and I have a question about how to find the entropy of a particular system. The system is a lattice of paramagnetic atoms fixed to the lattice sites, with an external ...
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1answer
25 views

Why is molar specific heat at constant volume of a monatomic ideal gas a constant?

I thought specific heat varies depending on the substance. Why is it always $(3/2) R$?
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32 views

Applying Statistical Mechanics to Formulate Corrosion (Rusting)

I wanted to try and take my current knowledge of statistical mechanics (first quarter undergraduate course completed, beginning researcher in far from equilibrium statistical mechanics, basic ...
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31 views

Periodic ground state 1-dim ising model

Good evening! I'm at the beginning of my study about the Ising model and it has been proposed to me this problem: Find all periodic ground-state configuration for the following one-dimensional Ising ...
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31 views

How can one approximate integral def. of Z by the max value of the integrand?

I am taking a course in statistical physics, and while reviewing my notes from the lectures I came across something that I cannot get my head around. We arrive at an integral expression for the ...
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1answer
36 views

Subtraction In Quadrature?

I have a system of particles (electrons) with an initial RMS energy spread (say "1"). It goes through a section of constant magnetic field (bend magnet) and the electrons radiate. The electrons lose ...
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1answer
26 views

Change in entropy adiabatic expansion

I think that an adiabatic expansion of a gas should cause the entropy to increase. On the other hand we have for adiabatic processes that $dQ = 0$ and therefore $dS= 0$, which is why I thought that ...
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3answers
48 views

Change in energy ideal gas

I am supposed to calculate the change in energy upon changing both the temperature from $T_1$ to $T_2$ and the volume from $V_1$ to $V_2$. Now I was wondering whether this solution is correct: We ...
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55 views

From Quantum Mechanics to Statistical Mechanics in a Specific Case

I'd like to know how to get to statistical mechanics from the many-particle Schrodinger equation using a specific example, without using any Hamiltonian mechanics, phase spaces or ensembles, as a ...
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74 views

Does QM needs refinement?

Suppose atoms of an ideal gas are represented by non overlapping wave function so that the system can be described classically. As time passes the packets spread. Therefore over a period of time we ...
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66 views

First law of thermodynamics [closed]

In the first law of thermodynamics, we learned that $W$ and $Q$ are path-dependent quantities, but how are $Q$ and $W$ defined? I mean $W = \int_{\gamma} p(s) ds$ would be one possibility, where ...
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19 views

Volume in NVT ensemble

While solving a problem of ideal gas in canonical ensemble, I got stuck into this one. It may sound silly though- Why $$\int d^{3N}q$$ equals to $V^N$ but not $V^{3N}$
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16 views

Schottky Anomaly - Heat Capacity

I'm having a little bit of a difficulty understanding the origins of the schottky anomaly at low temperatures in the heat capacity of certain materials with restricted energy levels. As I understand, ...
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21 views

Independent boson model with an arbitrary finite-dimensional impurity

The independent boson model consists of the following Hamiltonian: $$ H_s = E \sigma^z $$ $$ H_b = \sum_k \omega_k b^{\dagger}_kb_k $$ $$H_{sb} = \sigma^z \sum_k (g_k b_k + g_k^{\ast}b^{\dagger}_k).$$ ...
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61 views

Debye Model Density of States In One Dimension

I am trying to obtain the Density of states of the Debye model in one dimension I know the answer I am prepping for an exam and I am a bit stuck: The answer is: $\frac{L}{\pi*c_s}$ where $c_s$ is ...
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45 views

What is the density operator for an isothermal–isobaric ensemble (T,p,N)?

In the microcanonical ensemble $(E,V,N)$, the density operator is $$\hat{\rho}=\frac{\delta(\hat{H}-E\,\hat{I})}{Tr(\delta(\hat{H}-E\,\hat{I}))}$$ Where $\hat{H}$ is the Hamiltonian of the system and ...
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57 views

A simple experiment and the Maxwell-Boltzmann distribution

Consider two containers separated by a removable wall, each side of which is a perfect mirror for the gas in the respective container. Also the walls of the containers are ideal mirrors. In each ...
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41 views

chemical potential in BEC decreases in temperature

For a bose gas we can calculate the average number of particles through $$N = \int_0^\infty \rho(\varepsilon)n(\varepsilon) d\varepsilon$$ where $\rho(\varepsilon)$ is the particle density for energy ...
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Exorcism of Maxwell's Demon

I am possessed! Yes, with the thinking that if there is actually a Maxwell's Demon, then it would open the negligible weighted door which would ultimately make the second law invalid. But really can ...
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1answer
49 views

How does the movement of molecules change at the edge of a liquid?

I am thinking about how the velocity of molecules measured from a small region of space might change as the region of inquiry moves closer to the edge of a container. Ultimately I am thinking about MR ...
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1answer
72 views

What does Born Green equation signify physically?

What does Born Green equation obtained from YBG hierarchy for the equilibrium particle densities signify? I mean how can you model the equation into a physical problem?I understood the steps involved ...
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89 views

What it means to integrate over $n$ variables out of $N$, where $N>n$?

I was reading Theory of Simple Liquids, when I came across BBGKY hierarchy. In deriving the expression for the hierarchy, they integrate an integration of N variables over N-n variables to make the ...
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1answer
65 views

Maxwell's Inspiration to think about fields

I was looking at a Wikipedia article which had the following statement Atomists, notably James Clerk Maxwell and Ludwig Boltzmann, applied [...]. In modern literature Maxwell is often thought ...
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26 views

Johnson Noise: Source of thermal fluctuations

I've read a lot online about Johnson noise being caused by thermal fluctuations, and the Wikipedia page of thermal fluctuations attributes this to the fact that particles don't all have the same ...
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72 views

Calculate Helmholtz Free Energy with Entropy, Work given [closed]

it's my first time here and I hope the post complies with the general rules. My problem originates here: I'm doing a statistical physics task which unfortunately leaves me clueless atm. I keep my ...
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24 views

How velocity dispersion changes with change of inertial frame

I'm analysing a bunch of simulated galaxies, and one of the properties I'm looking at is their velocity dispersion (which is the same thing as the standard deviation of their speeds as far as I know). ...
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35 views

Derivation of ensemble distribution

I heard that you can derive the canonical ensemble by maximizing $L = \sum_i p_ilog( p_i ) + \alpha (\sum_i p_iE_i-E)$ or for the grand-canonical ensemble $L = \sum_i p_ilog( p_i ) + \alpha ...
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1answer
33 views

How did Planck use the concept of statistical entropy in trying to understand the meaning of his own law?

I was reading Introducing Quantum Theory: A graphic guide (by J.P.McEvoy & Oscar Zarate) and came across Planck's predicament of understanding his very own law that accurately explained the ...
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23 views

Examples of systems with linear response behavior

I've checking the linear response theory and there are 3 fundamental assumptions. 1) Linearity of the response of the system to an external excitation, 2) Stationary response function: ...
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2answers
74 views

How does the second law of thermodynamics follow from low entropy of early universe?

One of the explanations of the second law of thermodynamics is that it goes back to the low entropy in the early universe (How do you prove the second law of thermodynamics from statistical ...
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48 views

Equivalent tensor order parameters of nematic liquid crystals?

I found in the literatures two different definitions of the tensor order parameter of nematic liquid crystals. One is $$ Q_{ij}=\frac{S}{2}(3n_{i}n_{j}-\delta_{ij}), $$ where $S$ is the scalar order ...
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How did Rayleigh and Jeans apply the Equipartition of Energy in determining the energy distribution of blackbody - radiation? [duplicate]

I am reading the Ultraviolet Catastrophe and have come across this law. Here , it is written They applied the statistical physics method to the waves by analogy with Maxwell's gas particles using ...
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43 views

Relationship between Liouvile's theorem and Diffusion equation

Consider a Hamiltonian system. According to the Liouville's theorem there exists a probability density function $\rho(q^a,p_a,t)$ in the phase space whose evolution is given by $$ \frac{\partial \rho ...
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26 views

Mean square velocity of an ideal Bose gas

I'm trying to find the mean square velocity of a particle in an ideal Bose gas. The equation is given by: $\langle v^2 \rangle = \dfrac{1}{N}\displaystyle\sum_{\vec{k}}(\hbar ...
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9 views

How is the pattern of the decay of cluster expansion coefficient

For cluster expansion applied in material prediction. Is there some general trends how the ECIs should decay? Thank you.