When I say “arbitrary” I mean “including negative values”.
I think your notion of life as decreasing entropy density is clearly wrong, because black holes are maxentropy objects, black hole volume is proportional to cube of mass, but entropy is additive, i.e., proportional to mass, so density of entropy is decreasing with growth of black hole and black holes are certainly not alive under any reasonable definition of life. Or, you can take black holes in very far future, where they consist the most of the matter, and increasing-entropy evolution of the universe results in black hole evaporation, which decreases density of entropy to almost-zero.
I think your notion of life as decreasing entropy density is clearly wrong,
My notion wasn’t that life decreases entropy, my notion was that life increases entropy.
because black holes are maxentropy objects, black hole volume is proportional to cube of mass, but entropy is additive, i.e., proportional to mass, so density of entropy is decreasing with growth of black hole and black holes are certainly not alive under any reasonable definition of life.
Black holes seem like a suboptimal hypothetical since we don’t really know what’s going on inside them. Their entropy especially seems paradoxical.
Under my model, density of entropy ought to increase with the growth of life.
When I say “arbitrary” I mean “including negative values”.
I see. Though, what would that look like for Earth, using free energy to sort all the resources into separate bins? Which I suppose is something a utility maximizer might want. But are we really anywhere close to that? Maybe the theorem just doesn’t apply yet, since it’s only supposed to apply to a steady state.
When I say “arbitrary” I mean “including negative values”.
I think your notion of life as decreasing entropy density is clearly wrong, because black holes are maxentropy objects, black hole volume is proportional to cube of mass, but entropy is additive, i.e., proportional to mass, so density of entropy is decreasing with growth of black hole and black holes are certainly not alive under any reasonable definition of life. Or, you can take black holes in very far future, where they consist the most of the matter, and increasing-entropy evolution of the universe results in black hole evaporation, which decreases density of entropy to almost-zero.
My notion wasn’t that life decreases entropy, my notion was that life increases entropy.
Black holes seem like a suboptimal hypothetical since we don’t really know what’s going on inside them. Their entropy especially seems paradoxical.
Under my model, density of entropy ought to increase with the growth of life.
I see. Though, what would that look like for Earth, using free energy to sort all the resources into separate bins? Which I suppose is something a utility maximizer might want. But are we really anywhere close to that? Maybe the theorem just doesn’t apply yet, since it’s only supposed to apply to a steady state.