As everyone knows, when two objects at different temperatures get in contact, heat will flow from the hotter to the colder object, until temperatures equilibrate. This fact constitutes the second law of thermodynamics. The same happens also for information: it can only go from the `informed’ party (i.e., where the information is stored) to the `uninformed’ one. This intuition can be formalized as a data-processing principle.

The above arguments hide, however, an implicit assumption — that the two objects (or information carriers) never met in the past, i.e., are uncorrelated. Indeed, in the presence of initial correlations, anomalous backward flows of heat/information have been predicted and observed, in violation of the data-processing principle.

However, not all correlations enable such anomalous flows. For example, purely classical correlations do not have such ability. Hence the question naturally arises: which correlations allow to break the data-processing principle?

In this paper I present a general characterization of such correlations from an information-theoretic viewpoint. The main discovery is that the situation is much richer than previously thought: not only the quality but also the quantity of correlations matters — the delicate tradeoff between them being given by the condition of complete positivity, a central concept in quantum mechanics.

The hope is that the approach I propose here, unifying a number of previous works and thus simplifying the global picture, will contribute to the understanding of the deep (though, in my opinion, not so straightforward, as claimed somewhere) connections between information theory, quantum theory, and thermodynamics.

This work will appear in Physical Review Letters. Pre-print available at http://arxiv.org/abs/1307.0363