On a general criterion for nonclassicality from a signaling perspective

We argue that the essence of nonclassicality of a bipartite correlation is a positive signal deficit-- the communication cost excess over the available signaling. By this criterion, while violations of Bell-type and contextuality inequalities are necessarily non-classical, some violations of the Leggett-Garg inequality are classical. Further, signaling tends to diminish nonclassical properties, such as intrinsic randomness, no-cloning, complementarity, etc. Signal deficit is shown to have its ultimate origin in intrinsic randomness. A possible analogy of nonclassicality to the metamathematical concept of Gödel incompleteness is noted.

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