Equation 19 · The Arrow of Time and the Engine of Evolution
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol T_in
n is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Symbol T_out
ut is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
subtraction
Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
How to interpret it
Read this expression with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
Kleidon’s framework treats this temperature drop the way an engineer treats any heat engine’s hot and cold reservoirs: the Carnot limit sets an absolute ceiling, ( - )/ , on what fraction of the incoming energy flux could in principle be converted to usable work rather than simply thermalized, and almost none of Earth’s actual energy conversions get anywhere near that ceiling — atmospheric convection and the hydrologic cycle instead settle, empirically, near a maximum power point that trades efficiency for a sustainable throughput [ 13 ] . Two channels intercept solar energy before it thermalizes at all rather than converting already-thermalized…
Read the full surrounding passage
Kleidon’s framework treats this temperature drop the way an engineer treats any heat engine’s hot and cold reservoirs: the Carnot limit sets an absolute ceiling, ( - )/ , on what fraction of the incoming energy flux could in principle be converted to usable work rather than simply thermalized, and almost none of Earth’s actual energy conversions get anywhere near that ceiling — atmospheric convection and the hydrologic cycle instead settle, empirically, near a maximum power point that trades efficiency for a sustainable throughput [ 13 ] . Two channels intercept solar energy before it thermalizes at all rather than converting already-thermalized heat: photosynthesis and photovoltaics, both of which capture free energy from excited electrons directly, before that energy degrades into random thermal motion. Photosynthesis is the one evolution built. Kleidon’s global analysis of terrestrial ecosystems puts the median efficiency of that capture, across more than thirteen thousand site-years of data, at roughly 0.78 percent of the solar free energy actually available for conversion — a figure the paper describes explicitly as “much lower than what thermodynamics would allow for” [ 14 ] . The gap between what the Carnot-type ceiling permits and what photosynthesis actually achieves is not evolution failing to optimize; it reflects that photosynthesis is constrained less by the ceiling itself than by the coupled costs of material exchange — water loss through the same stomata that admit carbon dioxide — that any biochemical implementation of light capture has to pay alongside it.
Sources cited in the surrounding passage
- [13] Working at the limit: a review of thermodynamics and optimality of the Earth system ↗
- [14] What limits photosynthesis? Identifying the thermodynamic constraints of the terrestrial biosphere within the Earth system ↗
These citations give research context. Read each source to check which claims it supports.
Return to The Arrow of Time and the Engine of Evolution