Black hole entropy divergence and the uncertainty principle

Black hole entropy has been shown by 't Hooft to diverge at the horizon. The region near the horizon is in a thermal state, so entropy is linear to energy which consequently also diverges. We find a similar divergence for the energy of the reduced density matrix of relativistic and non-relativistic field theories, extending previous results in quantum mechanics. This divergence is due to an infinitely sharp division between the observable and unobservable regions of space, and it stems from the position/momentum uncertainty relation in the same way that the momentum fluctuations of a precisely localized quantum particle diverge. We show that when the boundary between the observable and unobservable regions is smoothed the divergence is tamed. We argue that the divergence of black hole entropy can also be interpreted as a consequence of position/momentum uncertainty, and that 't Hooft's brick wall tames the divergence in the same way, by smoothing the boundary.Comment: Added clarifications and explanation

Entanglement and the Speed of Evolution in Mixed States

Entanglement speeds up evolution of a pure bipartite spin state, in line with the time energy uncertainty. However if the state is mixed this is not necessarily the case. We provide a counter example and point to other factors affecting evolution in mixed states, including classical correlations and entropy

Communication Systems Performance at mm and THz as a Function of a Rain Rate Probability Density Function Model

6G is already being planned and will employ much higher frequencies, leading to a revolutionary era in communication between people as well as things. It is well known that weather, especially rain, can cause increased attenuation of signal transmission for higher frequencies. The standard methods for evaluating the effect of rain on symbol error rate are based on long-term averaging. These methods are inaccurate, which results in an inefficient system design. This is critical regarding bandwidth scarcity and energy consumption and requires a more significant margin of effort to cope with the imprecision. Recently, we have developed a new and more precise method for calculating communication system performance in case of rain, using the probability density function of rain rate. For high rain rate (above 10 mm/h), for a typical set of parameters, our method shows the symbol error rate in this range to be higher by orders of magnitude than that found by ITU standard methods. Our model also indicates that sensing and measuring the rain rate probability is important in order to provide the required bit error rate to the users. This will enable the design of more efficient systems, enabling design of an adaptive system that will adjust itself to rain conditions in such a way that performance will be improved. To the best knowledge of the authors, this novel analysis is unique. It can constitute a more efficient performance metric for the new era of 6G communication and prevent disruption due to incorrect system design