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One observes that a considerable level of confusion remains about some ofthose aspects of irreversibility, entropy generation and `the arrow of time'which actually are well understood. This demands that great care must be takenin any discussion of irreversibility to use clear-cut notions and preciselanguage in order to be definite about which property follows from whichassumption. In this work, a novel toy model of `algebraic mechanics' ispresented that elucidates specific key aspects of entropy generation in asystem with extremely simple reversible fundamental dynamics. It is argued whyinsights gained through a detailed quantitative study of this toy model alsohave to be taken into account for any realistic model of microscopic dynamics,classical or quantum alike. As irreversibility also touches upon the quantummechanical measurement process (through the `proof' of the `H-Theorem'), asimple way to address the tenacious question `when (and how) the wave functioncollapses' is offered.

Algebraic mechanics as an accessible toy model demonstrating entropy generation from reversible microscopic dynamics