# What is Boltzmann: Definition and 210 Discussions

Ludwig Eduard Boltzmann (German pronunciation: [ˈluːtvɪg ˈbɔlt͡sman]; 20 February 1844 – 5 September 1906) was an Austrian physicist and philosopher. His greatest achievements were the development of statistical mechanics, and the statistical explanation of the second law of thermodynamics. In 1877 he provided the current definition of entropy,

S
=

k

B

ln

Ω

{\displaystyle S=k_{\rm {B}}\ln \Omega \!}
, interpreted as a measure of statistical disorder of a system. Max Planck named the constant kB the Boltzmann constant.Statistical mechanics is one of the pillars of modern physics. It describes how macroscopic observations (such as temperature and pressure) are related to microscopic parameters that fluctuate around an average. It connects thermodynamic quantities (such as heat capacity) to microscopic behavior, whereas, in classical thermodynamics, the only available option would be to measure and tabulate such quantities for various materials.

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1. ### I A Bold New Take on Quantum Theory

New Scientist recently published an article entitled 'A Bold New Take on Quantum Theory'. I found interesting Unfortunately, it is behind a paywall, but I will give my precis. How QM, which only predicts probabilities, gives rise to the solid, well-defined world around us is still a mystery...
2. ### A H-Theorem and Lagrange multipliers

so I was studying H theorem from Richard Fitzpartic's site. https://farside.ph.utexas.edu/teaching/plasma/Plasma/node35.html Given H, they consider the following equation and set the constants as I want to understand how they got these particular values for a, b &c can we consider the...
3. ### Thermal lattice Boltzmann model ignoring source term -- python code help please

LBM model for phase change- relevant equations found here. Also here. #Thermal LBM #solves 1D 1 phase phase-change #D2Q5 Lattice nx=100 # the number of nodes in x direction lattice direction ny=5 # the number of nodes in y...
4. ### A Quantum analog of Boltzmann entropy?

In classical statistical physics, entropy can be defined either as Boltzmann entropy or Gibbs entropy. In quantum statistical physics we have von Neumann entropy, which is a quantum analog of Gibbs entropy. Is there a quantum analog of Boltzmann entropy?
5. ### I Is there a Boltzmann distribution for a system with continuous energy?

Hi. I'm not sure where to put this question, thermodynamics or the quantum physics forum (or somewhere else). For a system in equillibrium with a heat bath at temperature T, the Boltzman distribution can be used. We have the probability of finding the system in state n is given by ##p_n =...
6. ### B Shape & Dimensions of Containers: Impact on the Maxwell Boltzmann Distribution

1.Does the Maxwell Boltzmann distribution change depending on the shape of the container? Pressure and the volume is constant. How is the Distribution affected whether the gas is in: a,sphere b,cube c,cuboid? Why does/doesn’t the distribution change depending on the shape of the container...
7. ### I Is the Boltzmann energy distribution an instance of energy diffusion?

I (mechanical engineer) have researched this question but can't get to an answer. The equilibrium condition for confined particle diffusion of a solute in a solvent is reached when the solute spatial density is uniform (= zero density gradient), and entropy is max. But per Boltzmann, when...
8. ### A Exact Boltzmann Factor - Comparing y1 & y2 w/ 7 & 8 Particles

Page 51 in <Moderator's note: link to copyrighted material removed, see instead http://dx.doi.org/10.1119/1.2967703> The image is showing functions: y1=e^(ln(n0)-x) y2=invDigamma(digamma(n0+1)-x)-1 where y2 is the "exact" version. How exactly is it exact? For this example (with 7 particles)...
9. ### A Resolve Discrepancies in Boltzmann's Equilibrium Theory

In Lectures on Gas Theory (Dover Books on Physics) (p. 74), Boltzmann states “In nature, the tendency of transformations is always to go from less probable to more probable states”, by which he means what are now called macrostates. Thus he claims that an ideal gas almost always evolves to the...
10. ### I Boltzmann Entropy Formula – Derivation

Boltzmann entropy definition is given by: $$S = k_B lnW$$ where ##W## is the weight of the configuration which has the maximum number of microstates. This equation is used everywhere in statistical thermodynamics and I saw it in the derivation of Gibbs entropy. However, I can't find the...
11. ### I Problem regarding understanding entropy

I was reading about thermodynamics postulates when i came over the differnetial fundamental equation: I understand that the second element is just pressure and last element is chemical energy, but he problem is i don't understand what is the use of entropy and how does it contribute to a...
12. ### I Boltzmann brains and limitless energy....

Hello! Amateur question alert! Please excuse any misuse of terms. Answers gratefully received. :smile: I have a question about the energy that can be drawn from the vacuum through quantum fluctuations. My understanding is there are very strict limits on how much energy can be borrowed for how...
13. ### I Validity of the Boltzmann Distribution

I (mechanical engineer) have researched this question but can't get to an answer. My question concerns the validity of the Boltzmann distribution. We start with "particles in a box". These particles (at t-zero) may exhibit a range of energies. We place this box of particles in a heat bath for...
14. ### Popular physics: Boltzmann Brains and Sci-Fi

I assume you people are all so preoccupied with all the hard sciencemastering going on that you're missing out on the more basic [sic] research abundantly present under the "Popular Physics" header at arxiv.org. Particularly: Futurama, Marvel's Supervillains and Boltzmann Brains. I'm not...

44. ### When is the Boltzmann equation applicable in a Fermi plasma?

When do we use the Boltzmann equation for density in a Fermi plasma? n in [cm-3] and when do we use the ρ=m/V, ρ in [Kg/m3 ] (this is not an example, I just added the equations to make my question more understandable) Is the ideal gas only when we have electron and ions? Is the Boltzmann...
45. ### I Exploring the Possibility of Boltzmann Brain Formation

‘Everything can happen, will happen’ so the saying goes. So given infinite time a universe is meant to generate infinite Boltzmann brains. But I was thinking about this: - Things that are possible can become impossible (example: heat death making Boltzmann brains formation impossible) -...
46. ### I Deriving the Boltzmann distribution

I was reading the derivation of Boltzmann distribution using the reservoir model. lets call the reservoir by index R and the tiny system by index A. In the derivation they proposed that the probability for being at energy e (for A) is proportional to the number of states in reservoir. I didn't...
47. ### I Boltzmann Distribution: Feynman's treatment of p-n junction

In Vol III, 14-4 and 14-5 of the Feynman Lectures (http://www.feynmanlectures.caltech.edu/III_14.html), Feynman gives a discussion of the p-n junction, in which he derives the diode characteristic equation via a nice, simple and convincing application of the Boltzmann distribution to the...
48. ### Statistical Mechanics Part II: The Ideal Gas - Comments

Greg Bernhardt submitted a new PF Insights post Statistical Mechanics Part II: The Ideal Gas Continue reading the Original PF Insights Post.
49. ### A Can indistinguishable particles obey Boltzmann statistics

Many textbooks claim that particles that obey Boltzmann statistics have to be indistinguishable in order to ensure an extensive expression for entropy. However, a first principle derivation using combinatorics gives the Boltzmann only for distinguishable and the Bose Einstein distribution for...
50. ### A Collision integral approximation in boltzmann equation

Hi, as you can see at the end of the picture/attached file collision integral is approximated to a discrete sum. Could you express how this approximation is derived?