# 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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### 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, ...
115 views

### A question on relaxation time approximation

I was learned that the form of collision term in relaxation time approximation is set to be: $$\left (\frac{\partial f}{\partial t}\right)_c=-\frac{f-f^0}{\tau}$$ in with $f^0$ is local equilibrium ...
1 vote
57 views

### How to find the time derivative of temparature by solving the relativistic Boltzmann equation?

I am trying to find the temporal derivatives of the temperature by solving the relativistic Boltzmann equation. However, it didn't turn out as simple as I thought. The relativistic Boltzmann equation ...
1 vote
51 views

### Verification of the second law of thermodynamics for liquids?

I have a pure math background and I am currently self-learning physics. To mathematically justify and understand the Second Law of Thermodynamics, mathematicians and physicists have studied the motion ...
114 views

### Why two systems with similar space of possible microstates have different entropy?

Boltzmann's entropy formula: $S=k_{\mathrm {B} }\ln \Omega$ where $\Omega$ is the number of real microstates corresponding to the gas's macrostate. Let's assume that we are talking about an ideal gas ...
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### Is nonlinearity a denser encoding of information?

At the microscopic level, an $n$-particle system in 3D can be described by the Liouville equation, which governs the evolution of the distribution function in a $6n$-dimensional phase space. Going ...
1 vote
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### Boltzmann equation for Lennard-Jones particles?

In the Vlasov variant of Boltzmann equation, the Coulomb pair forces are included via the force term that appears as the prefactor of the derivative of the density with respect to velocity. In that ...
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### From Newtonian mechanics to Boltzmann (or statistical) mechanics

Classical mechanical systems observable on a dynamical scale are subject to Newton's laws. In this case, knowledge of the Hamiltonian allows us to minimize energy taking into account inertia. This ...
1 vote
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### Value of Inverse of Thermal Voltage

I am trying to solve the Poisson-Boltzmann Equations and have come about the constant $$\beta = \frac{e}{K_BT}$$ which Wikipedia denotes as the inverse of Thermal voltage. Now this constant is ...
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