Bell inequalities limit the possible observations of non-communicating parties. Here, we present analogous inequalities for any number of communicating parties under the causal constraints of static causal order,definite causal order,and bi-causal order.All derived inequalities are remarkably simple. They correspond to upper bounds on the winning chance in graphical games:Given a specific directed graph over the parties, the parties are challenged to communicate along a randomly chosen arc. In the case of definite causal order, every game that we find is specified by a kefalopoda digraph.Based on this we define weakly causal correlations as those that satisfy all kefalopoda inequalities. We show that the problem of deciding whether some correlations are weakly causal is solvable in polynomial time in the number of parties.

We discuss a simple toy model which allows, in a natural way, for deriving central facts from thermodynamics such as its fundamental laws, including Carnot’s version of the second principle. Our viewpoint represents thermodynamic systems as binary strings, and it links their temperature to their Hamming weight. From this, we can reproduce the possibility of negative temperatures, the notion of equilibrium as the coïncidence of two notions of temperature — statistical versus structural —, as well as the zeroth law of thermodynamics (transitivity of the thermal-equilibrium relation), which we find to be redundant, as other authors, yet at the same time not to be universally valid.

It was first observed by John Bell that quantum theory predicts correlations between measurement outcomes that lie beyond the explanatory power of local hidden variable theories. These correlations have traditionally been studied extensively in the probabilistic framework. A drawback of this perspective is that one is then forced to use in a single argument the outcomes of mutually-exclusive measurements. One of us has initiated an alternative approach, invoking only data at hand, in order to circumvent this issue. In this factual view, which is based on Kol-mogorov complexity, we introduce mechanisms such as complexity amplification. We establish that this functionality is realizable, just as its probabilistic counterpart, hereby underlining that Bell correlations are a precious information-processing resource.

The paradigmatic view where information is seen as a more fundamental concept than the laws of physics leads to a different understanding of spacetime, where the causal order of events emerges from correlations between random variables representing physical quantities. In particular, such an information-theoretic approach does not enforce a global spacetime structure. By following this path, we conclude that perfect signaling correlations among three parties are possible which do not obey the restrictions imposed by global spacetime. We show this using a recent framework based on the sole assumptions that locally, quantum theory is valid and random variables can be described by probability distributions. Our result is of zero-error type and can be seen as an analog to a three-party appearance of quantum non-locality which manifests itself by satisfying a condition with certainty, whereas the same is impossible for any local theory.