A principle of hierarchical entropy maximization is proposed for generalized superstatistical systems, which are characterized by the existence of three levels of dynamics. If a generalized superstatistical system comprises a set of superstatistical subsystems, each made up of a set of cells, then the Boltzmann-Gibbs-Shannon entropy should be maximized first for each cell, second for each subsystem, and finally for the whole system. Hierarchical entropy maximization naturally reflects the sufficient time-scale separation between different dynamical levels and allows one to find the distribution of both the intensive parameter and the control parameter for the corresponding superstatistics. The hierarchical maximum entropy principle is applied to fluctuations of the photon Bose-Einstein condensate in a dye microcavity. This principle provides an alternative to the master equation approach recently applied to this problem. The possibility of constructing generalized superstatistics based on a statistics different from the Boltzmann-Gibbs statistics is pointed out.

A recent discovery of the periodic activity of the repeating fast radio burst source FRB 180916.J0158+65 in the Canadian Hydrogen Intensity Mapping Experiment (CHIME) hints at possible origin of the FRB from a freely precessing neutron star with a magnetar magnetic field of about 10¹⁶ G. However, the absence of simultaneously detected high-energy emission in the Swift and AGILE observations imposes stringent constraints on the field magnitude and questions the possibility of such a progenitor. We show that consideration of forced precession of a neutron star does not encounter the difficulty. This kind of precession takes place even if the neutron star is not deformed and is brought about by the anomalous moment of electromagnetic forces induced by stellar rotation and determined by non-corotational currents. Contrary to what is expected for the currents of corotation, the anomalous torque calculated by the direct method appears to be non-zero. If the observed 16.35-day period corresponds to the period of stellar precession, the inferred internal magnetic field appears to be about 6 × 10¹⁴ G for rotational period 1 s. For another possibly periodic FRB 121102 with 157-day period the magnetic field is even lower, 2 × 10¹⁴ G, thereby justifying earlier considerations and not ruling out the hypothesis of FRB origin from precessing neutron stars.

A theory of the collapse of a punctured antibubble is developed. The motion of the rim of air formed at the edge of the collapsing air film cannot be described by a potential flow and is characterized by high Reynolds numbers. The rim velocity is not constant but gradually decreases with time and is determined by the balance between the surface tension and hydrodynamic drag forces. A collapse equation is derived and solved. The agreement between the theory and existing experiments is shown.

New long-term Very Long Baseline Array observations of the well-known jet in the M87 radio galaxy at 43 GHz show that the jet experiences a sideways shift with an approximately 8–10 yr quasi-periodicity. Such jet wobbling can be indicative of a relativistic Lense–Thirring precession resulting from a tilted accretion disc. The wobbling period together with up-to-date kinematic data on jet rotation opens up the possibility for estimating angular momentum of the central supermassive black hole. In the case of a test-particle precession, the specific angular momentum is J/Mc = (2.7 ± 1.5) × 10¹⁴ cm, implying moderate dimensionless spin parameters a = 0.5 ± 0.3 and 0.31 ± 0.17 for controversial gas-dynamic and stellar-dynamic black hole masses. However, in the case of a solid-body-like precession, the spin parameter is much smaller for both masses, 0.15 ± 0.05. Rejecting this value on the basis of other independent spin estimations requires the existence of a magnetically arrested disc in M87.

The recent discovery of a radio-emitting neutron star with an ultralong spin period of 76 s, PSR J0901-4046, raises a fundamental question on how such a slowly rotating magnetized object can be active in the radio band. A canonical magnetic field of $1.3\times {10}^{14}\mathrm{G}$ estimated from the pulsar period and its time derivative is wholly insufficient for PSR J0901-4046 to operate. Consideration of a magnetic inclination angle of 10° estimated from the pulse width gives a higher magnetic field of $1.5\times {10}^{15}\mathrm{G}$, which is still an order of magnitude lower than the necessary minimum of $2.5\times {10}^{16}\mathrm{G}$ following from the death line for radio pulsars with magnetic fields exceeding the critical value $4.4\times {10}^{13}\mathrm{G}$. We show that if the observed microstructure of single pulses reflects relativistic beaming, the inferred surface magnetic field appears to be $3.2\times {10}^{16}\mathrm{G}$, and without this assumption it is no less than $2.7\times {10}^{16}\mathrm{G}$, which explains the existence of radio emission from PSR J0901-4046. This estimation makes PSR J0901-4046 a radio pulsar with the strongest magnetic field known and is a sign that PSR J0901-4046 slows down not by magnetic-dipole radiation, but rather by an electric current of 56 MA, when rotational energy is expended in accelerating charged particles over the polar cap.

Generalized superstatistics, i.e., a “statistics of superstatistics,” is proposed. A generalized superstatistical system comprises a set of superstatistical subsystems and represents a generalized hyperensemble. There exists a random control parameter that determines both the density of energy states and the distribution of the intensive parameter for each superstatistical subsystem, thereby forming the third, upper level of dynamics. Generalized superstatistics can be used for nonstationary nonequilibrium systems. The system in which a supercritical multitype age-dependent branching process takes place is an example of a nonstationary generalized superstatistical system. The theory is applied to pair production in a neutron star magnetosphere. DOI: http://dx.doi.org/10.1103/PhysRevE.84.051128 ©2011 American Physical Society