Equation 18 · The Arrow of Time and the Engine of Evolution
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Symbol k_mathrm B
athrm B is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Symbol T
T is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
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.
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That distinction — a hard inequality on what is thermodynamically permitted, as opposed to a causal story about why anything organizes itself to approach that permission — is the difference between England’s 2013 result, which is uncontroversial physics, and the more ambitious theory built on top of it two years later, which is not. The 2013 bound is compatible with, and in fact numerically consistent with, Bennett’s independent estimate that real biological replication machinery dissipates on the order of tens of T per step [ 4 ] — both results describe the same underlying fact, that copying is not free, from two different derivations three decades apart. Neither result, on its…
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That distinction — a hard inequality on what is thermodynamically permitted, as opposed to a causal story about why anything organizes itself to approach that permission — is the difference between England’s 2013 result, which is uncontroversial physics, and the more ambitious theory built on top of it two years later, which is not. The 2013 bound is compatible with, and in fact numerically consistent with, Bennett’s independent estimate that real biological replication machinery dissipates on the order of tens of T per step [ 4 ] — both results describe the same underlying fact, that copying is not free, from two different derivations three decades apart. Neither result, on its own, says anything about which replicators natural selection favors; that remains a question about differential reproduction and heredity, not about the minimum heat bill any replicator, favored or not, must pay to exist at all.
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