- #1
Tabasko633
- 20
- 0
Dear community,
I stumbled upon this ecology article (https://www.witpress.com/elibrary/dne/4/2/402, page 4) and have some confusion about a statement in there:
"Before further unpacking the formal defnition of entropy, one would be justifed in asking why not simply choose (1 – p) instead of [–log(p)] as the most appropriate measure of nonexistence? The answer is that the resultant product with p (that is [p – p²]) is perfectly symmetrical around the value p = 0.5. Calculations pursuant to such a symmetric combination would be capable of describing only a reversible universe. Boltzmann and Gibbs, however, were seeking to quantify an irreversible universe. By choosing the univariate convex logarithmic function, Boltzmann thereby imparted a bias to nonbeing over being. One notices, for example, that max[–xlog{x}] = {1/e} ≈ 0.37, so that the measure of indeterminacy is skewed towards lower values of pi"
So I know that the definition of entropy uses an logarithm to be additive, but I don't understand this argument. How can it be concluded that it therefore describes an irreversible universe?
I stumbled upon this ecology article (https://www.witpress.com/elibrary/dne/4/2/402, page 4) and have some confusion about a statement in there:
"Before further unpacking the formal defnition of entropy, one would be justifed in asking why not simply choose (1 – p) instead of [–log(p)] as the most appropriate measure of nonexistence? The answer is that the resultant product with p (that is [p – p²]) is perfectly symmetrical around the value p = 0.5. Calculations pursuant to such a symmetric combination would be capable of describing only a reversible universe. Boltzmann and Gibbs, however, were seeking to quantify an irreversible universe. By choosing the univariate convex logarithmic function, Boltzmann thereby imparted a bias to nonbeing over being. One notices, for example, that max[–xlog{x}] = {1/e} ≈ 0.37, so that the measure of indeterminacy is skewed towards lower values of pi"
So I know that the definition of entropy uses an logarithm to be additive, but I don't understand this argument. How can it be concluded that it therefore describes an irreversible universe?