174,769 research outputs found

    Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps

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    We introduce, and numerically study, a system of NN symplectically and globally coupled standard maps localized in a d=1d=1 lattice array. The global coupling is modulated through a factor rαr^{-\alpha}, being rr the distance between maps. Thus, interactions are {\it long-range} (nonintegrable) when 0α10\leq\alpha\leq1, and {\it short-range} (integrable) when α>1\alpha>1. We verify that the largest Lyapunov exponent λM\lambda_M scales as λMNκ(α)\lambda_{M} \propto N^{-\kappa(\alpha)}, where κ(α)\kappa(\alpha) is positive when interactions are long-range, yielding {\it weak chaos} in the thermodynamic limit NN\to\infty (hence λM0\lambda_M\to 0). In the short-range case, κ(α)\kappa(\alpha) appears to vanish, and the behaviour corresponds to {\it strong chaos}. We show that, for certain values of the control parameters of the system, long-lasting metastable states can be present. Their duration tct_c scales as tcNβ(α)t_c \propto N^{\beta(\alpha)}, where β(α)\beta(\alpha) appears to be numerically consistent with the following behavior: β>0\beta >0 for 0α<10 \le \alpha < 1, and zero for α1\alpha\ge 1. All these results exhibit major conjectures formulated within nonextensive statistical mechanics (NSM). Moreover, they exhibit strong similarity between the present discrete-time system, and the α\alpha-XY Hamiltonian ferromagnetic model, also studied in the frame of NSM.Comment: 8 pages, 5 figure

    A Schroedinger link between non-equilibrium thermodynamics and Fisher information

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    It is known that equilibrium thermodynamics can be deduced from a constrained Fisher information extemizing process. We show here that, more generally, both non-equilibrium and equilibrium thermodynamics can be obtained from such a Fisher treatment. Equilibrium thermodynamics corresponds to the ground state solution, and non-equilibrium thermodynamics corresponds to excited state solutions, of a Schroedinger wave equation (SWE). That equation appears as an output of the constrained variational process that extremizes Fisher information. Both equilibrium- and non-equilibrium situations can thereby be tackled by one formalism that clearly exhibits the fact that thermodynamics and quantum mechanics can both be expressed in terms of a formal SWE, out of a common informational basis.Comment: 12 pages, no figure