Questions tagged [boltzmann-equation]
DO NOT USE THIS TAG for Boltzmann's constant, Maxwell-Boltzmann distribution, Stefan-Boltzmann law & Boltzmann brains!
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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:
$$\int_{D_1}\left[{\frac{\partial F_N}{\partial t} +\sum_{i=1}^{N} {\vec{v}_i}.\frac{\partial F_N}{...
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Receipt for writing down the Boltzmann-equation for a given interaction
Suppose one has a gas consisting of two particles, which are known to primarily interact with each other through a specific interaction. To describe the behavior of the particle densities, I would ...
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3
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Boltzmann distributions on atomic orbitals: infinite degeneracy?
The (unnormalized) Boltzmann probability distribution of states as a function of energy and temperature is given by
$$P(\epsilon_i) \propto g_i\exp\left(\frac{-\epsilon_i}{k_BT}\right)$$
with $P(\...
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Assumption of molecular chaos (confusion)
The molecular chaos means that the velocities of the two particles are uncorrelated before the collision. However, this is no longer the case after the collision, which is why the whole problem with ...
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Is it possible to say that entropy would affect the charge transportation?
I noticed there are a few papers from Dr. Karuppuchamy Navamani, for example:
Generalization on Entropy-Ruled Charge and Energy Transport for Organic Solids and Biomolecular Aggregates
Theoretical ...
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Distribution of states of H$_2$ gas for a given temperature
How can I calculate the population distribution of vibrational and rotational states of H$_2$ gas, for any given temperature? I think the vibrational states are more important, since the rotational ...
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Conservation Equations Used in Boltzmann Transport Equation: Kardar
I am reading through the derivation of the Boltzmann transport equation in the text, Statistical Mechanics of Particles by Kardar. I am unable to make sense of the conservation equations described.
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Expressions for Entropy in the Canonical Ensemble
In the microcanonical ensemble, we have the standard Boltzmann expression for entropy:
\begin{equation}\label{1}
S = k_B\ln \Omega
\end{equation}
where $\Omega$ is the number of elements of the ...
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How is Weiss mean field approximation actually maximising the partition function of Boltzmann's distribution?
Considering other mean field approximation (e.g. Max entropy approach or $<S_i> = m_i
+\delta S_i$ , $\delta S_i \simeq0$), a common approach that I've seen is that of maximising the partition ...
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Definition of temperature in Boltzmann transport theory
In kinetic theory, the local temperature in a fluid is defined in terms of the average thermal energy of the particles, as
\begin{equation}
\langle E_{th}\rangle= \int {d^3v}\frac{1}{2} m|\mathbf v-\...
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Acoustic finite-size effects of simulated fluids under periodic boundary conditions
Consider a fluid simulated in a finite box of specific size. An impulse to the fluid element at the center in a given direction is physically expected to propagate at the speed of sound and attenuate ...
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"Boltzmann" equation for radiation (Reheating period)
These equations are given in many papers as the "Boltzmann equations" (without derivation) governing the reheating period, where $\rho_\phi$ is the energy density of the decaying inflaton ...
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Question about the Boltzmann Distribution for an ideal gas
The general statement of the Boltzmann distribution law is that for a system of $N$ particles, each having access to energy states $\varepsilon_1,\varepsilon_2,\dots,\varepsilon_k$, the ratio the ...
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Is there a way to express the collisionless boltzmann equation in terms of positions, velocities, times, without the distribution function?
Suppose I have data that represents a field of positions and velocities. If the distribution function (DF) for the data is $f(x,v,t)$, I know that the DF must obey
$$\frac{\partial f}{\partial t} + \...
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Difference between thermodynamical, statistical, and dynamical equilibrium
I have two related questions concerning the difference between thermodynamic, statistical mechanical, and dynamical equilibrium. In particular, I am thinking about the statistical physics of galaxies, ...
