This followup discusses fluid simulation related information reduction in view of time irreversibility of the governing evolution equations.

We gain an overview of a statistical perspective on the microscopic motion and highlight the implied time irreversibility as well as the exclusion of antidissipation.

Topics covered/used: Kinetic Theory of Gases, Boltzmann Equation, OneParticle Phase Space Density Function, Information Reduction, Laws of Evolution, Microscopic and Macroscopic Perspective, Laws of Motion, Time Reversibility vs. Time Irreversibility, Dissipation.

Timetable:

00:00 Microscopic Motion vs. Macroscopic Experience
01:33 Macroscopic Influence on Microscopic Motion and Dissipative Tendency
04:38 Statistical Perspective on Microscopic Motion and Information Reduction
08:54 Time Irreversibility of the Statistical Perspective
10:13 What's coming next? (Fluid Simulation Series!)


Important Note:

I recommend exploring the literature further (see a few selected references below), as there are many more aspects necessary to fully understand the nature of time irreversibility, which may be covered in an extended version of this part. In particular, for brevity, I have chosen not to introduce the nparticle phasespace density perspective here, useful to talk about densities of (anti)trajectories what could be done to define dissipation and related concepts probabilistically. This is addressed more verbally by saying things like "some antitime behavior", implying that probabilities should not be attached to individual trajectories, but rather that one should think in terms of probability densities. For the short version, I have tried to convey such aspects at least verbally, but if you are interested, you should know that there is of course much more to say.


Selected Papers and Learning Resources:

Book: Evans, Denis James, Debra Joy Searles, and Stephen Rodney Williams. Fundamentals of classical statistical thermodynamics: dissipation, relaxation, and fluctuation theorems. John Wiley & Sons, 2016.

Book: Hoover, William Graham, and Carol Griswold Hoover. Time reversibility, computer simulation, algorithms, chaos. Vol. 13. World Scientific, 2012.

Paper: Lebowitz, Joel L. "Boltzmann's entropy and time's arrow." Physics today 46 (1993): 3232.

Paper: Ardourel, Vincent. "Irreversibility in the derivation of the Boltzmann equation." Foundations of Physics 47.4 (2017): 471489.

Paper: Maes, Christian, and Karel Netočný. "Timereversal and entropy." Journal of statistical physics 110.1 (2003): 269310.

Lecture Notes: from "http://volkov.eng.ua.edu/ME591_491_NE..." to "NEGD06"

Lecture Notes: "Kenkre, V. M.. Statistical Mechanics. https://www.unm.edu/~aierides/505/" specifically ".../bbgky2.pdf" & ".../bbgky3.pdf"

Lecture Notes: "Cerfon, Antoine. Mechanics (Classical and Quantum). https://www.math.nyu.edu/~cerfon/mech..."


Disclaimer:

This series focuses specifically on the aspect of information reduction in dynamical systems. For the sake of clarity, I had to omit many interesting aspects of the topics addressed in the video. So, the video itself is a reduction. :)

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