zoobyshoe said:
So, you have two bank accounts. Every day the same amount is deposited in each, and every day the same amount is withdrawn from each. Assuming the withdrawals equal the deposits, both accounts end up with whatever they had when you started. So, whichever was warmer when you started will be the warmer when you end.
England, though, is saying one system could change to both receive and pay out more than the other. In other words: a proper gedanken can't limit what the "bio" area takes in and puts out, because that pre-emptively prevents the very thing he claims will happen: greater intake and exhaust. One of his contentions is that living things replicate so that yet more energy can be taken in and shed. So, you also couldn't contain the "bio" area, because that would prevent the inhabitants from replicating beyond a certain point. The gedanken has to be designed so that both terrariums are allowed to take in and exhaust as much energy as they "want" and to expand their area if they need to. I think the 2000 year result is obvious.
I agree with your point.
What I left to the reader in my first post, I'll answer here. In the specific case where each terrarium receives the same total energy (from sunlight) per day, and each terrarium also emits the same
total energy per day (whether that be by reflected sunlight, or by heat, or by any other means), the temperature of two terrariums will remain equal. The first law of thermodynamics guarantees that. So we're both in agreement there.
But what I alluded to in my first post and prodded a bit more in my second post is the difference between classical and quantum versions of entropy. We need to consider not only the energy leaving each system, but the
entropy leaving each system. Let's use the bank account analogy.
I like your bank account analogy, by the way!
In classical thermodynamics, there is no differentiation when it comes to subdivisions of energy. Two half divisions of energy is the same as one whole division of energy as far as entropy goes. In classical thermodynamics, energy never comes in discrete chunks so it's all the same. Quantum entropy takes each chunk into account. That said, let's go back to the bank account.
Suppose I have two bank accounts (and for the sake of argument, suppose the bank accounts are from different banks). Every day I deposit a $1000 American dollar bill in each bank account. Also every day I withdraw $1000 dollars from each bank account, but in different denominations:
Bank account A: I withdraw ten, $100 bills per day.
Bank account B: I withdraw one hundred, $10 bills per day.
It's obvious that both bank accounts are maintaining the same balance. But which bank is producing the most
entropy?
(Classical thermodynamics cannot distinguish between the two. But quantum versions of entropy [accepting the limitations of the analogy] might.)