# 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.

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### Is flowing with RG in 1D Ising model equivalent to changing the temperature of the system

Let us consider the easiest form of the Ising Hamiltonian: $$\beta H(s_i; J) = -J\sum_i^N s_i s_{i+1}$$ ($\beta = 1/k_BT$ so we already defined $J = \tilde{J}/k_BT$ with $\tilde{J}$ constant). ...
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### Vacuum chamber end plate thicknees calculation [closed]

How to calculate the thickness of the flat covers used in the cylindrical vacuum chamber.
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### Why are the microstates of a harmonic oscillator considered equally probable, when the particle spends more time at locations of zero momentum?

Introductory statistical mechanics for a microcanonical ensemble (a.k.a. constant energy, no exchange of heat or work with environment) claims that all microstates in the momentum–location phase space ...
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### Summing graphs in the partition function (statistical physics)

I am looking at Tong's lecture notes on statistical physics, and I wanted to understand a step in his cluster expansion better. The goal here is to calculate the partition function in the canonical ...
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### Is the concept of entropy a result of limited technology?

I know that entropy is the energy within a system that is unable to do useful work. However, there was a time in which we were unable to harness the energy of the wind or the sun, and now we can, ...
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I've got very much confused about distributions and am looking for quick help. Distributions are common in physics, so I humbly hope to receive an answer that will resolve my confusion. Let's suppose ...
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### If electric field inside a conductor is always zero, then why do free electrons move?

Electric field inside the conductor is zero. That means there is no electric force on electrons inside. Then how do free electrons move from atom to atom in random direction? What is the reason of ...
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1 vote
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### Free energy of a one-dimensional harmonic oscillator

The potential energy of a one-dimensional harmonic potential can be expressed as $U(x)=\frac{1}{2}K(x-x_0)^2$, where $K$ is the force constant and $x_0$ is the equilibrium position. I'm wondering how ...
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### Does Hawking radiation have a statistical physics origin like the usual derivation of Boltzmann factors?

According to Andrew Steane's Thermodynamics chapter 19 on Thermal radiation: "The total emission from a physical object can usefully be separated in two parts: the thermal radiation and the rest. ...
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### Why does the CMB have a spectrum like a black-body radiation?

Equilibrium distributions of particles (Maxwell, Boltzmann, Saha) are achieved by the particle collisions. On the other hand, photons do not interact with each other. From the introductory course in ...
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1 vote
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### Normally distributing particle velocities

I'm trying to set up initial conditions for a collection of N particles distributed on the surface of a unit sphere so that they are uniformly distributed in position and their velocities are normally ...
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### Beyond the energy equipartition, what is the uneven law?

There is a celebrated energy equipartition theorem, it works fine for many systems. But it requires the dense filling of the surface of constant energy. What if there are other conserved quantities, ...
1 vote
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### Phonon Distribution Factor in Phonon Emission Rate

The rate at which a phonon with wavevector $\vec{q}$ is absorbed is given by $$\frac{1}\tau \propto n(\hbar \omega(\vec{q}))$$ This is pretty obvious to me. The more phonons there are the more often ...
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### Second law of thermodynamics and Unitarity of quantum mechanics [duplicate]

From the second law of thermodynamics, we know the entropy must be increasing in an isolated system, such as our Universe. On the other hand, we have quantum mechanics which, I think, somehow tells us ...
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### Measurements on macroscopic objects [duplicate]

I know that macroscopic objects undergo measurements continuously from the environment in which they are placed. I also know that in a quantum computer one can make a measurement of only a few qubits. ...
1 vote
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### Number of microstates for a specific energy for $N$-particle system subdividing energy into small intervals

I was reading a part of Reif's Statistical Physics book that said that the number of microstates for a system containing $N$ particle and energy $E$ is proportional to $δE$ but I am confused here. if ...
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### How can we explain expanding gas temperature at the microscopic level?

An insulated piston and cylinder contains an ideal gas. We pull the piston and expand the gas volume inside the cylinder. I understand the temperature drops due to this expansion. But, how can we ...
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1 vote
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### Gas temperature in a constant volume

An insulated container (constant volume, adiabatic) contains an ideal gas. We open the container's hatch for a few seconds and let some particles escape from the container, then we close the hatch. We ...
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### Standard deviation of kinetic energy approaches average kinetic energy

I have a simulated system of lots of particles modeled as circles moving in 2 dimensions. They bounce off each other and off of walls. Momentum and kinetic energy are conserved. I noticed that the ...
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### Adiabatic theorem with stochastic variables

Suppose a system which is driven by a stochastic complex variable $\alpha$(t). Looking at the eigensystem, both eigenvectors and eigenvalues are then stochastic variables. In my case, after building a ...
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