Do endothermic organisms have higher entropy or greater entropy production than ectotherms?
I've studied endothermy and ectothermy but I have never seen this topic contextualized in terms of physical entropy, and a preliminary literature search returns no results. I suppose this question is quite interdisciplinary...maybe if I finish What Is Life? Schrödinger will tell me, but I figured I would ask the panel and see if anyone has anything insightful to say.
Posted Oct 19, 2016, 4:36 AM UTC · edited
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Entropy production is pretty straightforward. Any spontaneous transfer of heat means that the total entropy is increasing. If we assume the animal is doing no work on the environment, the loss of heat dQ by the animal lowers its entropy by dSa >= -dQ/Ta and raises the entropy of the environment by dSe >= dQ/Te . The total the entropy gained for a transfer of heat dQ will therefore be:
∆S = dSa+dSa >= dQ(1/Te - 1/Ta)
This change in entropy is larger if the difference in temperature is larger (which is true for endotherms) and if the total heat lost is larger (which is also true for endotherms, at least compared to an ectotherm of comparable size).
So endotherms almost certainly produce more entropy. You can get extra entropy beyond this minimum required by the heat transfer, say by mixing two different gases together that were separated. But it is unlikely that these processes will amount to much compared to the heat generated.
The internal entropy of the organism is going to depend on its temperature as well, so my intuition is that an endotherm has more internal entropy than a comparably sized ectotherm. But trying to calculate the internal entropy for a system that complex is going to be nearly impossible, so I wouldn't want to say anything definite.
Under this view, are animals like partially isolated pockets of the Earth that may decrease their own local entropy temporarily, but that act to increase the Earth's total entropy as a whole? Particularly once the animal has died and decayed?
Yes, but that has to be true for any pocket of the world we can draw a box around. Total entropy is going up, even if it may go down inside the pocket.
One big simplification above is that I what I wrote is also true for an animal that, say, had just died. As the heat leaves the animal, total entropy goes up even as internal entropy decreases. In a living animal, new internal energy is being created by its metabolism to make up for the heat that is lost. I was worried about trying to define how much that might be, so I just left the lower limit in there. But, if we assume that the animal returns to roughly the same internal state after 24 hours (i.e. eats and digests about the same amount, keeps the same body temperature), then dSa should add to zero over that window.
That puts an even higher lower limit on the entropy created, namely:
∆S >= dQ/Te
Again, the endotherm still generates more entropy under this assumption because it released more heat over the course of a day.
We could get more detailed, and worry about the exact exchange of atoms between animal and environment as it breathes and eats and calculate chemical potentials for everything exchanged. This raises the lower limit on ∆S even further. But the endotherm is always doing more - releasing more heat, eating more food, exhaling more CO2 - so its lower limit goes up faster than the lower limit for the ectotherm.
Thank you for the detailed responses, this has been helpful. How did you learn this information--do you have any recommendations for texts or other resources?
I think "An introduction to thermal physics" by Schroeder is a good place to start:
https://www.amazon.com/Introduction-Thermal-Physics-Daniel-Schroeder/dp/0201380277
Mostly I was invoking the thermodynamic identity, which is described here.