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In our bio class our teacher told us that entropy was the amount of heat lost by a system. But I had learned before that entropy was like chaos / disorder in a closed system. Which definition Is right, or does entropy have different definitions in biology and physics?

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  • $\begingroup$ Your bio teacher was wrong if they said entropy was the amount of heat lost by a system. Rather, you can calculate the change in entropy of a system by dividing the heat flow into the system by its temperature. This is the thermodynamics version. In statistical mechanics, you learn that entropy is a measure of the number of ways a system can be configured at a particular energy, roughly speaking. It turns out that these definitions are equivalent, but there's way too much to say, making this question a little too broad, I think. $\endgroup$ – march Oct 30 '15 at 4:06
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    $\begingroup$ Entropy is not disorder. $\endgroup$ – user36790 Oct 30 '15 at 4:23
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    $\begingroup$ Related & possible duplicates:physics.stackexchange.com/questions/131170/… , physics.stackexchange.com/questions/52569/… , physics.stackexchange.com/questions/81857/…. $\endgroup$ – user36790 Oct 30 '15 at 4:24
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The definition of entropy can be found on Wikipedia. It's the integral of the reversible heat flow divided by the temperature at which the flow occurs. This has, at face value, nothing to do with order and disorder because there is no obvious way to even define structure in thermodynamics.

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 link is given by the unproven and most likely unprovable ergodic hypothesis. 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.

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. 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.

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. 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. 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. We haven't even begun to scratch the mathematical surface of these things. 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... RUN!

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