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It is proven that the logarithmic negativity does not increase on averageunder positive partial transpose preserving (PPT) operation includingsubselection (a set of operations that incorporate local operations andclassical communication (LOCC) as a subset) and, in the process, a furtherproof is provided that the negativity does not increase on average under thesame set of operations. Given that the logarithmic negativity is obtained fromthe negativity applying a concave function and is itself not a convex quantitythis result is surprising as convexity is generally considered as describingthe local physical process of losing information. The role of convexity and inparticular its relation (or lack thereof) to physical processes is discussed inthis context.Comment: Replaced with published version which includes one figur

Logarithmic Negativity: A Full Entanglement Monotone That is not Convex