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In the case of neutral populations of fixed sizes in equilibrium whose genealogies are described by the Kingman $N$-coalescent back from time $t$ consider the associated processes of total tree length as $t$ increases. We show that the (c\'adl\'ag) process to which the sequence of compensated tree length processes converges as $N$ tends to infinity is a process of infinite quadratic variation; therefore this process cannot be a semimartingale. This answers a question posed in Pfaffelhuber etdoi:10.1214/ecp.v19-3318 fatcat:44kkw46dmrfpxcsnt7frgniy34