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Superstatistics [C. Beck and E.G.D. Cohen, Physica A 322, 267 (2003)] is a formalism aimed at describing statistical properties of a generic extensive quantity E in complex out-of-equilibrium systems in terms of a superposition of equilibrium canonical distributions weighted by a function P(beta) of the intensive thermodynamic quantity beta conjugate to E. It is commonly assumed that P(beta) is determined by the spatiotemporal dynamics of the system under consideration. In this work we show by examples that, in some cases fulfilling all the conditions for the superstatistics formalism to be applicable, P(beta) is actually affected also by the way the measurement of E is performed, and thus is not an intrinsic property of the system.
We consider two different proposals to generate a time series with the same non-Poisson distribution of waiting times, to which we refer to as renewal and modulation. We show that, in spite of the apparent statistical equivalence, the two time series
Labour productivity distribution (dispersion) is studied both theoretically and empirically. Superstatistics is presented as a natural theoretical framework for productivity. The demand index $kappa$ is proposed within this framework as a new busines
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
Fluctuations of energy and heat are investigated during the relaxation following the instantaneous temperature quench of an extended system. Results are obtained analytically for the Gaussian model and for the large $N$ model quenched below the criti
This note derives the various forms of entropy of systems subject to Olbert distributions (generalized Lorentzian probability distributions known as $kappa$-distributions) which are frequently observed particularly in high temperature plasmas. The ge