A canonical realization of the BMS (Bondi–Metzner–Sachs) algebra is given on the phase space of the classical real Klein–Gordon field. By assuming the finiteness of the generators of the Poincaré group, it is shown that a countable set of conserved quantities exists (supertranslations); this set transforms under a particular Lorentz representation, which is uniquely determined by the requirement of having an invariant four-dimensional subspace, which corresponds to the Poincaré translations. This Lorentz representation is infinite-dimensional, nonunitary, reducible and indecomposable. Its representation space is studied in some detail. It determines the structure constants of the infinite-dimensional canonical algebra of the Poincaré generators together with the infinite set of the new conserved quantities. It is shown that this algebra is isomorphic with that of the BMS group.

The short-term prediction of earthquakes is an essential issue connected with human life protection and related social and economic matters. Recent papers have provided some evidence of the link between the lithosphere, lower atmosphere, and ionosphere, even though with marginal statistical evidence. The basic coupling is hypothesized as being via the atmospheric gravity wave (AGW)/acoustic wave (AW) channel. In this paper we analyze a scenario of the low latitude earthquake (Mw = 6.9) which occurred in Indonesia on 5 August 2018, through a multi-instrumental approach, using ground and satellites high quality data. As a result, we derive a new analytical lithospheric–atmospheric–ionospheric–magnetospheric coupling model with the aim to provide quantitative indicators to interpret the observations around 6 h before and at the moment of the earthquake occurrence.

The use of transfer entropy has proven to be helpful in detecting which is the verse of dynamical driving in the interaction of two processes, X and Y . In this paper, we present a different normalization for the transfer entropy, which is capable of better detecting the information transfer direction. This new normalized transfer entropy is applied to the detection of the verse of energy flux transfer in a synthetic model of fluid turbulence, namely the Gledzer–Ohkitana–Yamada shell model. Indeed, this is a fully well-known model able to model the fully developed turbulence in the Fourier space, which is characterized by an energy cascade towards the small scales (large wavenumbers k), so that the application of the information-theory analysis to its outcome tests the reliability of the analysis tool rather than exploring the model physics. As a result, the presence of a direct cascade along the scales in the shell model and the locality of the interactions in the space of wavenumbers come out as expected, indicating the validity of this data analysis tool. In this context, the use of a normalized version of transfer entropy, able to account for the difference of the intrinsic randomness of the interacting processes, appears to perform better, being able to discriminate the wrong conclusions to which the “traditional” transfer entropy would drive.