Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [statistical-mechanics]

The study of large, complicated systems by means of statistics and probability theory, in order to extract average properties and to provide a connection between mechanics and thermodynamics.

1
vote
2answers
199 views

Can the entropy of mixing be negative? [closed]

There is a general notion that the entropy of mixing should always be positive (or zero if we are mixing exactly the same stuff). However, I have a seeming counterexample at hand. Consider a box ...
3
votes
1answer
57 views

Bose condensate in 4d

Could a boson gas condensate in a hypervolume $V$ in 4D? How can I find its critical temperature and the heat capacity? In the books it just said volume $V$, it does not specify the dimension. My ...
0
votes
2answers
42 views

Building temperature into the Hamiltonian

Given a quantum Hamiltonian $H$ (e.g. the quantum Ising Hamiltonian $H= -h\sum_{i}X_i-\sum_{\langle i,j\rangle}Z_iZ_j$): we know that at temperature $T$, the system is in the state: $$\rho(T) = e^{-H/...
1
vote
0answers
28 views

Quantum Nuclear Corrections

I am interested in calculating quantum nuclear corrections to energy profiles or free energy profiles. For example, say I perform a DFT simulation for some molecules, and I the energetic profile in ...
1
vote
2answers
69 views

Negative probabilities with Wigner quasi-probability distributions

I was toying with Wigner corrections to thermodynamic equilibrium. The semiclassical correction for the position probability density to second order in $\hbar$ is: $$P(x)= \text{e}^{-\beta V(x)}\left(...
1
vote
1answer
23 views

Reconciling various expressions of flux and flow in kinetic theory

There are a few expressions I have been shown to describe the flux $\vec{\Phi}_A$ of some quantity $A$ described in kinetic theory. I am having trouble understanding how they are related or if they ...
0
votes
2answers
82 views

Energy of harmonic oscillators

I've calculated the energy of a classical harmonic oscillator (HO) as: \begin{align*} \overline E = \overline{E_K} + \overline{E_P} = \frac{\overline{p^2}}{2m} + \frac{k\overline{x^2}}{2} = \frac{...
1
vote
1answer
41 views

Multiplicity of statistical weight of macrostates when combining systems in thermodynamics (Boltzmann entropy)

In my lecture notes, the Boltzmann entropy form was motivated as a valid form for entropy partly because it was extensive. However this hinges on the assumption that the statistical weight for a ...
2
votes
3answers
134 views

Confusion on real space renormalization group for Ising model on lattice

For the Ising model with only nearst neighbor interaction on square lattice, if we do the RG by integrating out half degree of freedom, then we would get a new Ising model with many kind of ...
1
vote
1answer
58 views

Introductory to statistical mechanics text query

In the text "Introduction to modern statistical mechanics" by Chandler the following is stated in the first chapter: Entropy obeys several other important properties as well. To derive them, ...
1
vote
0answers
39 views

Regarding this interpretation of the pair correlation function

On some lecture notes of the statistical mechanics of Fermi systems I found the following, specifically regarding spin 1/2 systems: The correlation function $$ g_{\uparrow\uparrow}(s) \equiv \...
0
votes
2answers
85 views

Why is -273.15 °C the low temperature limit for the universe? [closed]

According to Ideal Gas Law the lowest temperature of an ideal gas can be $-273.15 °C$. This temperature is also considered the lowest temperature in the universe. But it is the lowest possible ...
1
vote
2answers
60 views

Derivation of 2nd law of Thermodynamics from ergodicity assumption

In Wikipedia it is claimed that: Assumption of the ergodic hypothesis allows proof that certain types of perpetual motion machines of the second kind are impossible. Since perpetual motion ...
1
vote
0answers
34 views

Blackbody photon variance and number of modes [closed]

In an experiment to measure the photon statistics of thermal light, the radiation from a black- body source is filtered with an interference filter of bandwidth 0.1 nm centered at 500 nm, and allowed ...
1
vote
0answers
30 views

Indistinguishable particles and statistical mechanincs

i'm studying the paragraph 5.5 (page 119) of this book: http://sciold.ui.ac.ir/~sjalali/MSc.Students/statistical.mechanics/pathria.pdf Now at page 121 we have: $$ \sum\limits_{p} \delta_p{u_{k1}}(...
3
votes
2answers
61 views

Chemical Potential and interactions

I'm interested in an model with interactions between different kind's of particles. Each particle species has it's own chemical potential. I want to treat the system in the Matsubara formalism. Here, ...
2
votes
1answer
47 views

Quantum statistics from the (anti)commutation relations of the operators?

From a QFT point of view, the difference between bosons and fermions is that their creation/annihilation operators ($a^{\dagger}$, $a$ and $c^{\dagger}$, $c^{\dagger}$ respectively) obey the following ...
1
vote
0answers
34 views

Many-body quantum tunneling: Is quantum tunneling sensitive to decoherence?

If we have a many-particle System that is strongly correlated, the tunneling probability can significantly increase; see this article here: https://www.sciencedaily.com/releases/2014/06/140612142215....
1
vote
1answer
188 views

Why the chemical potential of phonon gas in Einstein 's solid model is not zero

In Einstein’s model of solid, each atom in the solid is considered to be an independent three-dimensional quantum harmonic oscillator with characteristic frequency $ω$ that is constant. Each degree of ...
2
votes
1answer
59 views

Why do we study the Ising model on $\mathbb{Z}^d$ for $d > 3$?

I'm a beginner in statistical physics and I'm reading some stuff about the Ising model. So this might be a silly question. My question is: why we study the Ising model for high dimension cases, ...
7
votes
0answers
114 views

What are good books covering information theoretic approaches to theoretical physics?

I am about to finish my undergraduate studies and am very interested in going into the applications of information theory to either general relativity, or quantum mechanics. However I have been ...
-1
votes
0answers
23 views

How do the fluctuations of the order parameter depends on the dimensionality of the system?

In Landau theory of second order phase transitions, how do the fluctuations of the order parameter depends on the dimensionality of the system? In superconductors, the fluctuations of the order ...
1
vote
1answer
51 views

What is the probability distribution for a subsystem in canonical ensemble?

Suppose we have a 3d Ising Model(NN interaction) in simple cubic lattice, if we define a subsystem of it to be a 2d plane of spins(for example all sites with z = L/2, L being the linear system size) ...
1
vote
1answer
55 views

Phase transtions. Why has Ehrenfest classification been replaced by modern classification?

Why did modern classification replace Ehrenfest classification? What are the advantages of the modern one?
0
votes
0answers
50 views

Shot noise derivation

In the lecture notes I use to study on shot noise I found the following derivation for the Fourier transform of $$\phi_{shot} (t) = \langle (I(t+t_0)-\langle I\rangle)(I(t_0)-\langle I\rangle)\rangle =...
3
votes
2answers
178 views

What is the potential of mean force?

I've come across the term potential of mean force (PMF) in polymer physics, colloidal physics etc., but have not come across a complete definition. As far as I understand, the PMF determines the ...
2
votes
2answers
57 views

Why gas molecules move with different speed at a given tempreture?

As per my understanding we know that molecules of an ideal gas are identical in all aspects (size, shape, mass). Since collisions are elastic in nature, they don't lose their kinetic energy. That ...
1
vote
0answers
98 views

Path integrals vs operator

I have a statement that the path integrals formalism is eqivalent to operator formalism in quantum mechanics. Is it a correct statement? I understand that each of these two formalisms has its ...
3
votes
1answer
47 views

Reference Request - Modern Polymer Dynamics

I'm an applied math graduate student studying the cytoskeleton. I wanted to know of any reference(s) providing the most general mathematical theory of polymer dynamics, think an updated version of Doi ...
0
votes
0answers
60 views

Derivation of the Euler fluid equation

I'm currently taking a class on Thermodynamics where we now briefly touched upon Hydrodynamics. On of the major points of the chapter is deriving the Euler fluid equation and there I found my self a ...
0
votes
1answer
54 views

Why does a system assume ground state at absolute zero temperature?

I am going through Huang, Statistical Mechanics. He says at 0 kelvin, a quantum system assumes ground state so that $S=k_B ln(G)$ holds where $G$ is the degeneracy of the ground state . My question ...
-1
votes
1answer
68 views

Chemical equilibrium for a $2-2$ scattering and Boltzmann equation in cosmology and astroparticle physics

Definition of chemical equilibrium According to the definition of chemical equilibrium in Wikipedia, it is a situation where the rate of the forward reaction is same as the rate of backward reaction ...
1
vote
2answers
52 views
1
vote
1answer
71 views

Why are RG flow fixed points associated with different phases?

Why are RG flow fixed points associated with different phases? I thought the RG makes only statements about behavior near to critical points... a definite phase is far away from the critical point, ...
1
vote
0answers
51 views

Statistical physics at very large particle number

According to this manuscript http://www.math.lmu.de/~michel/credits/Federica_Pezzotti_phd.pdf it is proposed (e.g. at page 18) that particle correlations between particles can be neglected in the ...
0
votes
1answer
65 views

Implementing a Monte Carlo Simulation for the Gaussian Model

I want to implement a Monte Carlo simulation of the 1D Gaussian Model (the continuous generalisation of the Ising Model). That is the statistical mechanical model with the following Hamiltonian: $$ H ...
1
vote
0answers
23 views

Looking For a Relativistic Probability Distribution for Rotational Velocities of polyatomic molecules

I've been trying to find a suitable probability distribution function for the rotational velocity of molecules around T = 300K. It doesn't need to be incorporate QM effects, though I don't mind if it ...
1
vote
0answers
110 views

An idea to model a one-dimensional thermometer?

Let's say I have a $1$-dimensional material with thermal expansion $\alpha$: $$ \alpha l_0 = \frac{\Delta l}{\Delta T}$$ where $l$ is the length of the system and $T$ is it's temperature. This is ...
0
votes
1answer
44 views

Meaning of the uniform ensemble

In statistical physics (and viewing this from a classical point of view) for an isolated system we can say that a system will have an energy constant in time. People define the following uniform ...
1
vote
0answers
57 views

Phase fluctuations electromagnetic field

The electric field strength is given by: $$E(t)=E_0 \exp(i(\omega t + \phi(t))),$$ where $\phi(t)=\sqrt{2D} \ \Gamma(t)$. $D$ is the diffusion constant and $\Gamma(t)$ the line width. We have to ...
2
votes
0answers
52 views

Advected Dirac comb with random number of teeth which are born and die

I'm looking for a topic which I struggle to put into words. It's a reasonable consideration which I expect has been carefully studied. I hope someone can tell me the name of it and offer some guidance ...
4
votes
1answer
56 views

Defining work in a general, non-quasistic process involving thermal interaction

Is it possible, even in theory, to determine the work done and the heat exchanged in a general, non-quasistatic process? Example situation: Consider a tube separated into two sides A and B by a ...
2
votes
2answers
82 views

Why don't all gasses have infinite entropy? [duplicate]

Entropy of an ideal gas is defined as the logarithm of the number of possible states the gas can have multiplied by Boltzmann's constant: $${\displaystyle S=k_{\mathrm {B} }\log \Omega .}$$ In ...
5
votes
6answers
515 views

Explain the second principle of thermodynamics without the notion of entropy

I will teach some basic physics concepts to a group of university students not having to do with maths, physics, engineering and the like (mainly students of law, of political sciences and of similar ...
2
votes
1answer
51 views

High temperature expansion in general

I'm referencing this thesis which should be open-access. In Appendix D.1 "High temperature expansion in general", the author writes the high temperature expansion in the following way: $$ \begin{...
3
votes
1answer
90 views

Where does the principle of equal a priori probabilities come from in statistical mechanics?

I have studied that the principle of equal a priori probabilities yields maximum entropy principle and minimum free energy principle and we can define and calculate other thermodynamic variables. ...
0
votes
1answer
52 views

Carnot cycle with isometric processes

Consider the following slightly modified Carnot cycle with two extra isochoric processes for an ideal gas of adiabatic constant $\gamma$ working between temperatures $T_H>T_C$. A pV diagram is ...
1
vote
1answer
81 views

Phase transition in a 2D classical Heisenberg model Monte Carlo simulation

I have performed a Monte Carlo simulation of the classical Heisenberg model for a simple 2D square lattice. But I obtain some strange results. In fact, there is clearly a phase transition and a ...
1
vote
1answer
32 views

Question about ergodicity and the evolution of the probability distribution under Liouville's theorem

According to Liouville's theorem, the probability distribution function $\rho$ evolve in phase space with $$ \frac{d \rho}{d t} = \frac{\partial \rho}{\partial t}+\left\{\rho,H\right\}_{P.B} =0 $$ ...
0
votes
1answer
45 views

Energy density, pressure and temperature for massive neutrinos in cosmology

I want to be able to numerically compute the mean energy density and pressure for a massive neutrino species in cosmology, at any given scale factor $a$. These are given in terms of the distribution ...