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Questions tagged [statistical-mechanics]

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

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Is there a method to represent the ground state of the Toric code for large sizes? [closed]

In the case of a system with $n$ spins, the vector size becomes $2^n$ if you use the Kronecker product. Thus, it seems impossible for me to create a quantum state using tools like MATLAB for systems ...
QM24's user avatar
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Distributing 3 distinct particles among 4 distinct energy states

Essentially, the question boils down to this: "Do we need to consider the order of distinct particles occupying the same energy level in a quantum system ?" For further clarification, I have ...
Leibniz's Alien's user avatar
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Relation between electron temperature and electronic mode of energy for a gas

I have been doing some introductory reading on plasma physics as part of my research, and I am currently trying to understand the concept of electron temperature. Based on my basic understanding, ...
Nikkhil Chander's user avatar
3 votes
2 answers
468 views

Physical meaning of symmetric and antisymmetric wavefunction

On describing Bosons and Fermions, the symmetry of wavefunction is introduced first. Here, If two particles a and b, are in two states n and k respectively, we get the wavefunction individually. On ...
Rajesh R's user avatar
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Thermal flunctuations of density in thermal equlibrium? [closed]

According to physics a fluid or gas in thermal equilibrium is not exactly homogeneous. Locally its density undergoes random fluctuations which are small compared to the corresponding equilibrium value....
stackdk93's user avatar
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Is the energy spectrum of molecules of an ideal gas at equilibrium in an isolated system the Maxwell-Boltzmann distribution? [closed]

The energy spectrum of an ideal gas at equilibrium in a closed system at thermal equilibrium with its surroundings is described by the Maxwell-Boltzmann distribution. If the system is then isolated ...
Arthur Goldman's user avatar
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Does detailed balance apply if electrons and ions have different temperatures

Suppose I have a plasma where the ion temperature $T_i$ is different from the electron temperature $T_e$. Does detailed balance still exist between recombination and ionization?
S.T. Zweig's user avatar
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The usage of temperature in quantum mechanics

This is a follow up question for my previous question, because now I am more confused than I was before. In a regular quantum mechanics course, temperature plays no role as it does not appear in the ...
MathMath's user avatar
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Difference between boundary conditions in thermodynamic limit

Consider a model for a spin chain. I somehow am able to find a general formula for the expectation value of some observable in both periodic and open boundary conditions. ie., under PBC, I have $\...
Souroy's user avatar
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What is the physical meaning of the average value of the long product of spin operators

For the quantum one-dimensional XYZ Heisenberg model with $N$ spins $1/2$, consider the following average values of the products of successive operators $\hat{\sigma}^x$ in the ground state $$ C_j(n) =...
Gec's user avatar
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When is the temperature relevant for a quantum many body system?

Let me illustrate my question with an example. Suppose I want to consider a system of $N$ identical bosons. The Hamiltonian of the system is typically of the form: $$H_{N} = \sum_{j=1}^{N}(-\Delta_{x_{...
MathMath's user avatar
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Where can I find the derivation of the law of mass action for liquids?

I already asked this in chemistry and all they gave me was a link to the historical derivation. https://chemistry.stackexchange.com/q/68195/ But this derivation relies on the Maxwell-Botlzmann ...
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When does equilibrium mean accessible microstates are represented with equal probability in an ensemble of systems?

I'm confused to when a system in equilibrium is to be found in any one of its acessible states with equal probability (accoriding to the postulate of equal a priori probabilities). Reif in his book ...
David's user avatar
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Ising Model magnetisation

I am simulating the 2D Ising Model and specifically looking at the time evolution of magnetisation $m$. Now, in the non-equilibrium state, magnetisation will grow as a power law with time $t$, if ...
Principia Mathematica's user avatar
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Definition of heat from stat phys [duplicate]

I don't really understand how to couple the idea of entropy as info with heat. Let's say that you have an isolated system. A cube with a a series of movable partitions parallel to a face of the curve. ...
Lina Jane's user avatar
6 votes
3 answers
691 views

Trouble understanding the classic approximation of a black body as a hole on a cavity

While studying the Rayleigh-Jeans attempt to explain the spectral energy distribution of black bodies I have trouble understanding the concept of a black body as a small hole on a cavity. We define a ...
Eva S's user avatar
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Equilibrium in physics

We know that harmonic oscillator or pendulum will not reach a equilibrium at infinite time. But why a system of gas molecules reaches equilibrium (entropy of an isolated system will tend to increase ...
Mantu Das's user avatar
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1 answer
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Will a Modified Maxwellian Demon Experiment Using Charged Particles Be Able to Recycle Heat?

(If necessary this experiment can be conducted in an environment where gravity is negligible to avoid gravitational effects.) Two adjacent containers are filled with a homogenous gas composed of ...
Jacob Miller's user avatar
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Why Does Every Member of the Ensemble Perform Work Equal to the Change in Free Energy During a Quasiequilibrium Process?

I'm studying Jarzynski's 1997 paper on the Jarzynski Equality. In the second part of the proof (from equation (9) to equation (10) in the paper), Jarzynski considers the following process: considering ...
Luessiaw's user avatar
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5 answers
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How to turn a sum into an integral?

In, An Introduction to Thermal Physics, page 235, Schroder wants to evaluate the partition function $$Z_{tot}=\sum_0^\infty (2j+1)e^{-j(j+1)\epsilon/kT}$$ in the limit that $kT\gg\epsilon$, thus he ...
GedankenExperimentalist's user avatar
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1 answer
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Argument for relationship between density of states and degrees of freedom and energy

From Reif's Fundamentals of Statistical and Thermal Physics chapter 2.5 Behaviour of the density of states: Can anyone give a clear explanation for why the density of varies rapidly as Energy ($E$) ...
David's user avatar
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Diffusive momentum transport as overlap of acoustic peaks?

In the context of molecular dynamics simulations of soft or hard spheres in the fluid phase (e.g., with Lennard-Jones interactions), it is known that the velocity autocorrelation function (VACF) ...
YoussefMabrouk's user avatar
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Why can we use Bose-Einstein statistics in this expression for number density

In a system with $N$ particles in some volume $V$ in contact with a reservoir of temperature $T$, we find that $$\bar{n_i}=\frac{g_i}{e^{\frac{{\epsilon}_i -\mu}{kT}} \pm 1}$$ depending on whether the ...
user62783's user avatar
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Are strong correlations of boundary spins possible in the absence of long-range order in the bulk?

Question about one-dimensional models with short range interaction of quantum spins, such as transverse Ising and Heisenberg models. Are there any examples when, in the ground state of the system, the ...
Gec's user avatar
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3 votes
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Path integral at large time

From the path integral of a QFT: $$Z=\int D\phi e^{-S[\phi]}$$ What is a nice argument to say that when we study the theory at large time $T$, this behaves as: $$ Z \to e^{-TE_0} $$ where $E_0$ is the ...
BVquantization's user avatar
2 votes
0 answers
33 views

Correlation function of a two-level quantum system coupled to a thermal bath

I am trying to quantify the temporal correlations of observables in an open quantum system, i.e. calculate a quantity of the type, \begin{equation} \langle n(t) n(t') \rangle - \langle n(t)\rangle \...
A G P's user avatar
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1 answer
112 views

Solid-on-solid models

I'm currently wondering about the so-called Chui-Weeks model 1 2, given by $$ H = J \sum_i |h_i - h_{i+1}| + K\sum_i \delta_{0,h_i}, $$ which is a type of solid-on-solid (SOS) model used to describe ...
Wladislaw Krinitsin's user avatar
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1 answer
70 views

Can ideal gas equation $PV = nRT$ be used in the intermediate stages of a irreversible and reversible process?

Suppose we have two processes, one is reversible and the other is irreversible. The ideal gas undergoes from state A to state B in both processes. I want to know that can I apply the formula $PV = nRT$...
Divyanshu Dwivedi's user avatar
1 vote
1 answer
84 views

How can the Lindblad master equation model decoherence?

In some references that I have read, a crucial assumption in deriving the Lindblad master equation is that the system and environment remain separable for all time. Hence, the system and environment ...
Silly Goose's user avatar
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9 votes
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Imagining Graham's number in your head collapses your head to a black hole

My question is how does the above phenomenon, as mentioned in Numberphile here, occur in a semi-quantitative way through physical laws. (i.e saying statistical mechanics implies that is not ...
Mahammad Yusifov's user avatar
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1 answer
45 views

What is the distribution of speeds in an ideal liquid?

By ideal, I mean similar conditions to the ideal gas-in-a-box with perfect spherical perfectly elastic homogenous atoms, so no inter-atomic forces, evaporation, gravity, rotations or phase changes. ...
monosodiumg's user avatar
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32 views

During evaporation, why would we expect temperature of the gas at the interface to be lower than the temperature of the liquid?

This paper says that, from the kinetic theory of gases, we expect temperature of the gas at the interface to be lower than the temperature of the liquid. Could the experts here please explain it? ...
Ritesh Singh's user avatar
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1 vote
1 answer
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Gibbs Free Energy and Definitions of Entropy [duplicate]

When we speak about entropy, it's classically defined as $\delta S = \frac {\delta Q}{T}$ Where, I emphasize that it's the definition for only a change in entropy and not entropy itself (That's how I ...
BlackKnight23's user avatar
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1 answer
59 views

Why does entropy obey the superposition principle?

I was deriving the Boltzmann's entropy formula $${\displaystyle S=k_{\mathrm {B} }\ln \Omega}$$ We start with two prepositions: Let's consider two systems and we know the entropy of the first is $S_1$...
User198's user avatar
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3 votes
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Definition of entropy and microstates (Huang)

The definition of Boltzmann entropy given in Ref. 1 appears to be different from most sources I've seen up to this moment. Let me start from the latter: typically textbooks assume that in a given ...
Mr. Feynman's user avatar
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2 votes
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Precise relation between theromdynamic beta and coupling constant in Euclidean QFT

In statistical mechanics, the thermodynamic is inverse of the temperature: $\beta \propto T^{-1}$. In Euclidean QFT, I have often run into the expression like $\beta \propto g^{-2}$ where $g$ is the ...
Keith's user avatar
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1 vote
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29 views

Bubble behaviour during water / vapour coexistence in the most idealised scenario without boundaries

Consider the following statement: during a 1st order phase transition, the temperature of the system stays constant and any extra heat goes into turning a larger portion of the system into the new ...
Rudyard's user avatar
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1 answer
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Why the interaction between system and thermal bath does not affect the energy levels of the system?

When we write down the full Hamiltonian of a system in contact with a thermal bath, it is as follows: $$H_{\text{total}} = H_{\text{system}} + H_{\text{system+bath}} + H_{\text{bath}}.$$ As our focus ...
user135580's user avatar
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2 votes
1 answer
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How does the extra term and sign change come from in Harold Grad’s derivation of Boltzmann’s equation? [closed]

Harold Grad’s method of deriving the Boltzmann equation starts by integrating the Liouville equation: $$\int_{D_1}\left[{\frac{\partial F_N}{\partial t} +\sum_{i=1}^{N} {\vec{v}_i}.\frac{\partial F_N}{...
Jyotishraj Thoudam's user avatar
1 vote
1 answer
121 views

Lagrange Multiplier as chemical potential in Lagrangian Density

Within Matsubara formalism, we often add one chemical potential term to our Lagrangian density: $\mu\phi^\dagger\phi$, claiming that the chemical potential $\mu$ is one Lagrange multiplier. But at ...
JinH's user avatar
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1 answer
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Feasibility of entropy at zero temperature

I remember a college lecturer of mine once gave me this equation of entropy during one of his lectures on thermodynamics: $$ \begin{align*} \Delta{S} = \frac{ d {Q} }{T} \\ \end{align*} $$ I found out ...
groaking's user avatar
1 vote
1 answer
69 views

Why the work done by surrounding on the piston is same as average work done by surrounding on the gas inside the cylinder? [closed]

In thermodynamics when we derive the formula for work done by the surrounding on the gas, we actually derive the formula for work done by the surrounding on the piston and say that let the surrounding ...
Virender Bhardwaj's user avatar
6 votes
2 answers
291 views

Does life erode Earth's mass over time?

Since life converts matter to energy, and there's no natural process that does the opposite (aside from supernovas), does this mean that the mass of our planet is gradually diminishing? I asked ...
Lynx's user avatar
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physical interpratation of partition function in Quantym field theory

Partition function in Statistical mechanics is given by $$ Z = \sum_ne^{-\beta E_n} $$ For QFT, it is defined in terms of a path integral: $$ Z = \int D\phi e^{-S[\phi]} $$ How can we see the relation ...
BVquantization's user avatar
2 votes
0 answers
45 views

Universality and continuous variation of critical exponent close to a tricritical point

A tricritical point is a point at which a second order transition line and a first order transition line merge. At equilibrium, this point can be described by a landau potential (see for example this ...
Syrocco's user avatar
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3 votes
1 answer
101 views

How to obtain "canonical form" of the following master equation?

I am following this paper (arXiv). The master equation given on page 4 (top left) reads: \begin{align} \dot{\rho} &= [2\gamma(t) + \bar{\gamma}(t)] [2 \sigma_x \rho \sigma_x + 2 \sigma_y \rho \...
phy_std's user avatar
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What systems/subsystems does statistical mechanics actually apply to?

I've been trying to start learning statistical mechanics but I've run into a few roadblocks with the terminology being used and need clarification before I continue. Specifically, I want to clarify ...
user62783's user avatar
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0 votes
2 answers
75 views

How much information is encoded in a ball on a field? [closed]

Consider a soccer ball placed on a planar field of finite dimension (just like a soccer field). How much information can be realistically encoded in the position of the ball on the field?
Noumeno's user avatar
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1 vote
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70 views

Intuition for imaginary time Greens function

I understand that $$G^M(0,0^+) = \operatorname{tr}\{\rho O_2 O_1\}$$ (I am not putting hats on the operators here because they don't render in the correct position) is simply the expectation value of ...
Rooky's user avatar
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Receipt for writing down the Boltzmann-equation for a given interaction

Suppose one has a gas consisting of two particles, which are known to primarily interact with each other through a specific interaction. To describe the behavior of the particle densities, I would ...
Luca D's user avatar
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