The logarithmic negativity is a full entanglement monotone that is not convex. The paper proves that the logarithmic negativity does not increase on average under general positive partial transpose preserving (PPT) operations, which includes local operations and classical communication (LOCC) as a subset. This result is surprising because convexity is generally considered to describe the local physical process of losing information. The paper discusses the role of convexity and its relation to physical processes, emphasizing the importance of continuity in this context. Entanglement is a key resource in quantum information processing, and its quantification is important for understanding its properties. The paper discusses the constraints on operations that manipulate quantum states, noting that LOCC operations are natural in communication settings. Under PPT operations, distillable quantum states become a valuable resource while bound entanglement is free. An entanglement monotone is a function that does not increase on average under LOCC or PPT operations. The negativity, defined as $ N(\rho) = \frac{||\rho^{\Gamma_{A}}||_{1}-1}{2} $, is an entanglement monotone. The logarithmic negativity, defined as $ LN(\rho) = \log||\rho^{\Gamma}||_{1} $, is an upper bound to distillable entanglement and has an operational interpretation. However, it is not convex, which led to the belief that it is not an entanglement monotone. The paper provides a rigorous proof that both the negativity and the logarithmic negativity are entanglement monotones under LOCC and PPT operations. The paper discusses the convexity issues and the relationship between convexity and physical processes. It shows that the lack of convexity alone is not sufficient to destroy monotonicity in the sense of eq. (1). The key observation is that convexity is a mathematical requirement for entanglement monotones and generally does not correspond to a physical process describing the loss of information about a quantum system. The concavity in combination with the monotonicity of the logarithm permits the proof of the non-increase of the logarithmic negativity under PPT operations. The paper concludes that the logarithmic negativity is a full entanglement monotone despite not being convex or concave.The logarithmic negativity is a full entanglement monotone that is not convex. The paper proves that the logarithmic negativity does not increase on average under general positive partial transpose preserving (PPT) operations, which includes local operations and classical communication (LOCC) as a subset. This result is surprising because convexity is generally considered to describe the local physical process of losing information. The paper discusses the role of convexity and its relation to physical processes, emphasizing the importance of continuity in this context. Entanglement is a key resource in quantum information processing, and its quantification is important for understanding its properties. The paper discusses the constraints on operations that manipulate quantum states, noting that LOCC operations are natural in communication settings. Under PPT operations, distillable quantum states become a valuable resource while bound entanglement is free. An entanglement monotone is a function that does not increase on average under LOCC or PPT operations. The negativity, defined as $ N(\rho) = \frac{||\rho^{\Gamma_{A}}||_{1}-1}{2} $, is an entanglement monotone. The logarithmic negativity, defined as $ LN(\rho) = \log||\rho^{\Gamma}||_{1} $, is an upper bound to distillable entanglement and has an operational interpretation. However, it is not convex, which led to the belief that it is not an entanglement monotone. The paper provides a rigorous proof that both the negativity and the logarithmic negativity are entanglement monotones under LOCC and PPT operations. The paper discusses the convexity issues and the relationship between convexity and physical processes. It shows that the lack of convexity alone is not sufficient to destroy monotonicity in the sense of eq. (1). The key observation is that convexity is a mathematical requirement for entanglement monotones and generally does not correspond to a physical process describing the loss of information about a quantum system. The concavity in combination with the monotonicity of the logarithm permits the proof of the non-increase of the logarithmic negativity under PPT operations. The paper concludes that the logarithmic negativity is a full entanglement monotone despite not being convex or concave.