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.
If black hole entropy seems paradoxical to you, then I don’t think you’ve really understood the concept. It’s because we have no idea what’s going on inside a black hole that they are maxentropy objects. Every possible microstate (internal arrangement of matter and energy) corresponds to the same macrostate (mass, charge, angular momentum, linear momentum). The natural logarithm of the number of possible microstates that corresponds to the current macrostate, times Boltzman’s constant, is the entropy, and black hole necessarily maximize that.
Living things increase entropy in their environment, for sure, because they consume free energy in order to preserve the low-entropy aspects of their own internal structure. If this seems in contrast with what you’ve been told or taught about life to date, then I suspect you haven’t had very good teachers.
Over time, internal entropy of an organism will increase until it dies, because the self-preservation and repair mechanisms are not perfect. But at any given moment, if you killed the organism, it would decay until it reached equilibrium with its environment, and the entropy of what used to be its body would increase more and faster. This is because the living organism had been acting to keep its own entropy lower than it would be otherwise.
If black hole entropy seems paradoxical to you, then I don’t think you’ve really understood the concept. It’s because we have no idea what’s going on inside a black hole that they are maxentropy objects. Every possible microstate (internal arrangement of matter and energy) corresponds to the same macrostate (mass, charge, angular momentum, linear momentum). The natural logarithm of the number of possible microstates that corresponds to the current macrostate, times Boltzman’s constant, is the entropy, and black hole necessarily maximize that.
I understand what entropy is, but entropy is supposed to increase because the underlying dynamics are reversible, and so it’s paradoxical if black holes truly are identical, as that seems to imply the dynamics aren’t reversible.
they consume free energy in order to preserve the low-entropy aspects of their own internal structure.
What do you mean by “low-entropy aspects of their own internal structure”? Entropy is a scalar quantity. If e.g. the body temperature of an animal increases its entropy more than the cellular repetition etc. decreases its entropy, then the animal overall is increasing rather than decreasing entropy, and my point in the OP holds.
The underlying dynamics are reversible, if weirdly. Black holes have non-zero temperature and emit Hawking radiation, slowly evaporating in the process.
And yes, entropy is a scalar, and it’s well defined both an overall system and for each subset of that system. What keeps the entropy of a living thing lower than that of an undifferentiated soup of molecules? Structures that separate and organize those molecules. That’s what I mean by aspects.
Others have already noted that it seems like you’re asking a hard-to-parse set of nonstandard questions, so sorry for any misunderstandings on my part.
You’re right that internally, organisms control the production and flow of entropy, rather than the absolute entropy as such. So if you’re asking whether the entropy of the body is higher than it would be if it were cooled to a lower room temperature, then yes. But that means the answer to your question depends on whether the organism is currently in Phoenix in summer or Canada in winter, or whether it’s warm or cold blooded. I’m not sure this question is interesting in regards to how likely life was to evolve in the first place. I suspect not very.
We ought to expect entropy to increase, so a priori life is much more feasible if it increases entropy rather than decreasing entropy.
Is spontaneous freezing of ice at low temperature a violation of the second law? No, because as described you wouldn’t be measuring the same system over time. You’d be measuring “Water” one one side and “Ice but not the heat given off” on the other. This also is why most of the rest of your bullet points are not really related to the second law as such. You can’t count the entropy of O2 evolved in photosynthesis while ignoring that of the C and the H and the absorbed photons and the emitted waste heat.
Usually you don’t talk about entropy density rather than absolute entropy, but it’s unclear to me what it means for organisms to “locally” increase/decrease entropy if not by density.
It means, how fast is the total entropy of the combined system increasing, and where is the entropy going?
If I mix together (dissolve) a pile of food small molecules (Water, sugars, amino acids, fatty acids, glycerol, nucleic acids, mineral salts), with the same elemental composition and temperature as my body, which has higher entropy? The former.
If I cool the pile but add enough extra sugar that, if burned, would heat it to body temperature, then what’s the answer? I’m not sure. But if I did the sugar burning to raise the temperature, consumed ambient O2, and emitted CO2 and H2O in the process, then the resulting system (hot solution + emitted gases) has even more entropy than the initially-warm pile.
Over the course of my life, my body built itself up out of exactly those kinds of components, creating a lower-entropy-than-a-solution-of-food-molecules body and a high entropy stream of waste gases, liquids, solids, and heat. This is the sense in which bodies are low-entropy.
The answer to the deep problem of the black hole information paradox you’ve mentioned is: Information does leak out of a black hole, albeit likely in encrypted form, and importantly black holes don’t destroy information, they preserve information.
We don’t know how it’s leaked or how it gets out, we only have speculations on the process, but we do know it gets out eventually.
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.
If black hole entropy seems paradoxical to you, then I don’t think you’ve really understood the concept. It’s because we have no idea what’s going on inside a black hole that they are maxentropy objects. Every possible microstate (internal arrangement of matter and energy) corresponds to the same macrostate (mass, charge, angular momentum, linear momentum). The natural logarithm of the number of possible microstates that corresponds to the current macrostate, times Boltzman’s constant, is the entropy, and black hole necessarily maximize that.
Living things increase entropy in their environment, for sure, because they consume free energy in order to preserve the low-entropy aspects of their own internal structure. If this seems in contrast with what you’ve been told or taught about life to date, then I suspect you haven’t had very good teachers.
Over time, internal entropy of an organism will increase until it dies, because the self-preservation and repair mechanisms are not perfect. But at any given moment, if you killed the organism, it would decay until it reached equilibrium with its environment, and the entropy of what used to be its body would increase more and faster. This is because the living organism had been acting to keep its own entropy lower than it would be otherwise.
I understand what entropy is, but entropy is supposed to increase because the underlying dynamics are reversible, and so it’s paradoxical if black holes truly are identical, as that seems to imply the dynamics aren’t reversible.
What do you mean by “low-entropy aspects of their own internal structure”? Entropy is a scalar quantity. If e.g. the body temperature of an animal increases its entropy more than the cellular repetition etc. decreases its entropy, then the animal overall is increasing rather than decreasing entropy, and my point in the OP holds.
The underlying dynamics are reversible, if weirdly. Black holes have non-zero temperature and emit Hawking radiation, slowly evaporating in the process.
And yes, entropy is a scalar, and it’s well defined both an overall system and for each subset of that system. What keeps the entropy of a living thing lower than that of an undifferentiated soup of molecules? Structures that separate and organize those molecules. That’s what I mean by aspects.
Others have already noted that it seems like you’re asking a hard-to-parse set of nonstandard questions, so sorry for any misunderstandings on my part.
You’re right that internally, organisms control the production and flow of entropy, rather than the absolute entropy as such. So if you’re asking whether the entropy of the body is higher than it would be if it were cooled to a lower room temperature, then yes. But that means the answer to your question depends on whether the organism is currently in Phoenix in summer or Canada in winter, or whether it’s warm or cold blooded. I’m not sure this question is interesting in regards to how likely life was to evolve in the first place. I suspect not very.
Is spontaneous freezing of ice at low temperature a violation of the second law? No, because as described you wouldn’t be measuring the same system over time. You’d be measuring “Water” one one side and “Ice but not the heat given off” on the other. This also is why most of the rest of your bullet points are not really related to the second law as such. You can’t count the entropy of O2 evolved in photosynthesis while ignoring that of the C and the H and the absorbed photons and the emitted waste heat.
It means, how fast is the total entropy of the combined system increasing, and where is the entropy going?
If I mix together (dissolve) a pile of food small molecules (Water, sugars, amino acids, fatty acids, glycerol, nucleic acids, mineral salts), with the same elemental composition and temperature as my body, which has higher entropy? The former.
If I cool the pile but add enough extra sugar that, if burned, would heat it to body temperature, then what’s the answer? I’m not sure. But if I did the sugar burning to raise the temperature, consumed ambient O2, and emitted CO2 and H2O in the process, then the resulting system (hot solution + emitted gases) has even more entropy than the initially-warm pile.
Over the course of my life, my body built itself up out of exactly those kinds of components, creating a lower-entropy-than-a-solution-of-food-molecules body and a high entropy stream of waste gases, liquids, solids, and heat. This is the sense in which bodies are low-entropy.
The answer to the deep problem of the black hole information paradox you’ve mentioned is: Information does leak out of a black hole, albeit likely in encrypted form, and importantly black holes don’t destroy information, they preserve information.
We don’t know how it’s leaked or how it gets out, we only have speculations on the process, but we do know it gets out eventually.