Can't understand why the final result of this integration is positive

Question

So, this excerpt is from this paper: Thermodynamics as a theory of decision-making with information-processing costs, the final equation doesn't follow the math, since the final result is positive, can someone explain what's going on here, or if it is an error?

jensen paull · Accepted Answer · 2022-06-15 18:45:43Z

1

No idea what the physics is.

However does this answer your question?

$$-kT\ln(\frac{V'}{V}) = kT\ln(\frac{V}{V'}) = kT \ln(c)$$

Edit: I think with their definition of c, it should be

$$kT \ln(\frac{1}{c})$$

answered Jun 15, 2022 at 18:39

jensen paull

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$\begingroup$ This solution seems likely if haven't substituted V' = cV and they haven't even mentioned that those two c's are different. $\endgroup$
– Shailendra Patel
Jun 15, 2022 at 18:45
$\begingroup$ I agree, their solution is incorrect, I think. $\endgroup$
– jensen paull
Jun 15, 2022 at 18:48
$\begingroup$ After reading the paper again, I think that this equation is converting energy into information, and since information can't be negative, the final result is positive. -scientificamerican.com/article/energy-and-information The author has cited this paper while explaining about kT. $\endgroup$
– Shailendra Patel
Jun 16, 2022 at 14:21
$\begingroup$ That's indeed a typo. In the thesis (adaptiveagents.org/_media/papers/thesis.pdf, Eq 6.2, page 82) you'll find the correct derivation and motivation. $\endgroup$
– peortega
Apr 22, 2023 at 11:29

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