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Ensemble of initial conditions for nonlinear maps can be described in terms of entropy. This ensemble entropy shows an asymptotic linear growth with rate K. The rate K matches the logarithm of the corresponding asymptotic sensitivity to initial conditions lambda. The statistical formalism and the equality K=lambda can be extended to weakly chaotic systems by suitable and corresponding generalizations of the logarithm and of the entropy. Using the logistic map as a test case we consider a wide class of deformed statistical description which includes Tsallis, Abe and Kaniadakis proposals. The physical criterion of finite-entropy growth K strongly restricts the suitable entropies. We study how large is the region in parameter space where the generalized description is useful.
After a general discussion of the thermodynamics of conductive processes, we introduce specific observables enabling the connection of the diffusive transport properties with the microscopic dynamics. We solve the case of Brownian particles, both ana
We show that the onset of quantum chaos at infinite temperature in two many-body 1D lattice models, the perturbed spin-1/2 XXZ and Anderson models, is characterized by universal behavior. Specifically, we show that the onset of quantum chaos is marke
We propose a measure, which we call the dissipative spectral form factor (DSFF), to characterize the spectral statistics of non-Hermitian (and non-Unitary) matrices. We show that DSFF successfully diagnoses dissipative quantum chaos, and reveals corr
We review the occurrence of the patterns of the onset of chaos in low-dimensional nonlinear dissipative systems in leading topics of condensed matter physics and complex systems of various disciplines. We consider the dynamics associated with the att
We study many-body chaos in a (2+1)D relativistic scalar field theory at high temperatures in the classical statistical approximation, which captures the quantum critical regime and the thermal phase transition from an ordered to a disordered phase.