Maxwell-Boltzmann statistics, Bose-Einstein statistics and Fermi-Dirac statistics all describe how energy is distributed in different physical systems at a given temperature.

For example, Maxwell-Boltzmann statistics describes how the speeds of particles are distributed in an ideal gas.

The temperature of a gas is only a statistical average of the total energy of the gas. But at a given temperature, not all particles have the exact same speed as the average: some are higher and others lower than the average.

For a large number of particles however, the fraction of particles that will have a given speed at a given temperature is highly deterministic, and it is this that the distributions determine.

One of the main interest of learning those statistics is determining the probability, and therefore average speed, at which some event that requires a minimum energy to happen happens. For example, for a chemical reaction to happen, both input molecules need a certain speed to overcome the potential barrier of the reaction. Therefore, if we know how many particles have energy above some threshold, then we can estimate the speed of the reaction at a given temperature.

The three distributions can be summarized as:

A good conceptual starting point is to like the example that is mentioned at The Harvest of a Century by Siegmund Brandt (2008).

Consider a system with 2 particles and 3 states. Remember that:

Therefore, all the possible way to put those two particles in three states are for:

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On September 2024, GitHub forbade our China Dictatorship auto-reply bot, the reason given is because they forbid comment reply bots in general. Though it was cool to see a junior support staff person giving out what obviously triggered the action:before a more senior one took over.

Ciro was slightly saddened but not totally surprized by the bloodbath against him on the Reddit the threads he created:

So we observe once again the stupidity of deletionism towards anything that is considered controversial. The West is discussion fatigued, and would rather delete discussion than have it.

We also se people against you having freedom to moderate your own repositories as you like it, with bots or otherwise. Giving up freedoms for nothing, because "bot is evil".

Announcements:

I edited the VOD of the talk Aratu Week 2024 Talk by Ciro Santilli: My Best Random Projects about the CIA 2010 covert communication websites a bit and published it at: www.youtube.com/watch?v=TFfuzZC5Qpc.

Announcements:

Materials paywalled: www.cs.ox.ac.uk/teaching/courses/2022-2023/grl/

Materials paywalled. E.g.: www.cs.ox.ac.uk/teaching/courses/2023-2024/cads/