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COVID-19 Portal While this global health crisis continues to evolve, it can be useful to look to past pandemics to better understand how to respond today.Student Portal Britannica is the ultimate student resource for key school subjects like history, government, literature, and more.Demystified Videos In Demystified, Britannica has all the answers to your burning questions.This Time in History In these videos, find out what happened this month (or any month!) in history.#WTFact Videos In #WTFact Britannica shares some of the most bizarre facts we can find.Britannica Classics Check out these retro videos from Encyclopedia Britannica’s archives.Britannica Explains In these videos, Britannica explains a variety of topics and answers frequently asked questions.Thus my advice to you: when someone talks about entropy and it's not a chemical process engineer talking about the thermodynamic efficiency of the industrial chemical process that he is responsible for. We haven't even begun to scratch the mathematical surface of these things. What Newton couldn't know and what is not at all captured by terms like entropy is that there is a world of utterly complex dynamics between integrable mechanical systems and the thermodynamic limit. Physicists knew already at the end of the 19th century that this is not true and mathematically the "trouble" with dynamic systems was already known to Newton who failed to solve the three body problem. Part of the problem, as far as a I can tell, is that much of the discussion about the dynamics of physical (and biological!) systems is still being carried out at the level of the 19th century, when the world seemed divided into (and fully explainable by!) either mechanics or thermodynamics. However, while in physics entropy is extremely well defined in both thermodynamic and statistical mechanics terms, many characterizations in the layman literature seem questionable, at best, and there is quite a bit of overreach about the "meaning" and function of entropy IMHO. If we accept the ergodic hypothesis as "essentially correct" (in a physical, NOT in a strict mathematical sense), then we can recover thermodynamic entropy as a measure of order/disorder, which is definable in terms of counting microstates.
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While the ergodic hypothesis is quite plausible and physically very well realized for many systems, one can construct trivial cases for which it does not hold (especially for systems that are interaction free like the ideal gas), which should give us some pause with regards to the mathematical problem with ergodicity. This link is given by the unproven and most likely unprovable ergodic hypothesis. One has to understand the link between thermodynamics and statistical mechanics to get a sense of where the second meaning of entropy comes into play. This has, at face value, nothing to do with order and disorder because there is no obvious way to even define structure in thermodynamics. It's the integral of the reversible heat flow divided by the temperature at which the flow occurs. The definition of entropy can be found on Wikipedia.
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