A maximum entropy approach to H-theory: Statistical mechanics of hierarchical systems

A novel formalism, called H-theory, is applied to the problem of statistical equilibrium of a hierarchical complex system with multiple time and length scales. In this approach, the system is formally treated as being composed of a small subsystem---representing the region where the measurements are made---in contact with a set of `nested heat reservoirs' corresponding to the hierarchical structure of the system. The probability distribution function (pdf) of the fluctuating temperatures at each reservoir, conditioned on the temperature of the reservoir above it, is determined from a maximum entropy principle subject to appropriate constraints that describe the thermal equilibrium properties of the system. The marginal temperature distribution of the innermost reservoir is obtained by integrating over the conditional distributions of all larger scales, and the resulting pdf is written in analytical form in terms of certain special transcendental functions, known as the Fox $H$-functions. The distribution of states of the small subsystem is then computed by averaging the quasi-equilibrium Boltzmann distribution over the temperature of the innermost reservoir. This distribution can also be written in terms of $H$-functions. The general family of distributions reported here recovers, as particular cases, the stationary distributions recently obtained by Mac\^edo {\it et al.} [Phys.~Rev.~E {\bf 95}, 032315 (2017)] from a stochastic dynamical approach to the problem.Comment: 20 pages, 2 figure

Lower Mass Bound on the W′W^\prime mass via Neutrinoless Double Beta Decay in a 3-3-1 Model

The discovery of neutrino masses has raised the importance of studies in the context of neutrinoless double beta decay, which constitutes a landmark for lepton number violation. The standard interpretation is that the light massive neutrinos, that we observed oscillating in terrestrial experiments, mediate double beta decay. In the minimal 3-3-1 model, object of our study, there is an additional contribution that stems from the mixing between a new charged vector boson, $W^{\prime}$, and the Standard Model W boson. Even after setting this mixing to be very small, we show that tight constraints arise from the non-observation of neutrinoless double beta decay. Indeed, we derive bounds on the mass of the $W^{\prime}$ gauge boson that might exceed those from collider probes, and most importantly push the scale of symmetry breaking beyond its validity, leading to the exclusion of the minimal 3-3-1 model.Comment: 16 pages, 5 figure

Online Automated Synthesis of Compact Normative Systems

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