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Thermodynamic approaches to calculating the compute cost of evolution
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This type of approach, introduced by Ege Erdil, tries to estimate the total amount of energy irradiated towards the earth and convert this into FLOP. Erdil used the Landauer principle for this conversion. I consider this approach, and explain each of the parameters and how my estimates differ from his here (see his document here, please do not share outside of Epoch for now). In this spreadsheet, I extend this approach; whilst still using the earths energy budget, I consider different ways to convert this into FLOP, described below as the Caloric approach and brain energy approach. These are explored in detail under their corresponding tabs in this sheet.
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ApproachDescriptionEquation
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Landauer's principle"Landauer's principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. It holds that an irreversible change in information stored in a computer, such as merging two computational paths, dissipates a minimum amount of heat to its surroundings. In intuitive terms, this is the energy cost of information." (source)

The Landauer principle outlines the minimum amount of energy needed to run an operation without decreasing the overall entropy of a system (ie. without breaking the second law of thermodynamics). Thus, given some set of energy, if you assume that all of that energy was put into running operations, you can come out a number of operations that could have been possibly run. Using all of the energy budget of earth here is a huge overestimate, as not all of energy was put into running operations (much was wasted, much was converted into things like light, thermal, or kinetic energy and not into information). Operations can be also be seen as FLOP (the operations a computer undertakes) to calculate the maximum amount of FLOP that could have theoretically happened. 		FLOP= (Energy in the system) / (FLOP cost based on Landauer limit)

or

FLOP= (Energy in the system) / (k⋅T⋅ln(2))

​Note the Landauer limit is:
E=k*T*ln(2)
Where, E is the energy per bit (in joules), k is the Boltzmann constant, which is in joules per kelvin (J/K) and T is the temperature in kelvin.
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Caloric approach The caloric model determines the energy required to produce one FLOP by taking into account two factors: the average daily caloric intake of a human and the average FLOP/s performed by the brain. It divides the total daily calories by the number of seconds in a day to find out how much energy the human body uses every second. Using this information, it then calculates the energy cost of a single FLOP.
FLOP = (Energy in the system) / (FLOP cost based on caloric intake of an average human)
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Brain energy approachThe brain energy approach determines the energy required to produce one FLOP by taking into account two factors: the average amount of energy used by a human brain and the average FLOP/s performed by the brain. Using this information, it then calculates the energy cost of a single FLOP.
FLOP = (Energy in the system) / (FLOP cost based on energy used by the brain)
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