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As long as the Sun shines on (and this is essenty “for ever”), there is an increasing accumulation of energy in the planet: that is where the possibility of exponential “growth” comes.

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Your point is invalid because it would require an exponential growth of the sun power (the derivative of an exponential is an exponential). While the sun power is exponential around a billion years, it is a constant over a year. So you would reach at most a linear GDP growth.

Not so fast. Entropy is decreasing. There might be more energy, but useless energy. Energy low enough, spread out enough or with too little temperature differential that you can't do much or anything with it.

The Earth is getting solar energy sure. But it also emits energy. And a lot of what stays here is just useless heat.

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