174,769 research outputs found

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

We introduce, and numerically study, a system of $N$ symplectically and
globally coupled standard maps localized in a $d=1$ lattice array. The global
coupling is modulated through a factor $r^{-\alpha}$, being $r$ the distance
between maps. Thus, interactions are {\it long-range} (nonintegrable) when
$0\leq\alpha\leq1$, and {\it short-range} (integrable) when $\alpha>1$. We
verify that the largest Lyapunov exponent $\lambda_M$ scales as $\lambda_{M}
\propto N^{-\kappa(\alpha)}$, where $\kappa(\alpha)$ is positive when
interactions are long-range, yielding {\it weak chaos} in the thermodynamic
limit $N\to\infty$ (hence $\lambda_M\to 0$). In the short-range case,
$\kappa(\alpha)$ 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 $t_c$
scales as $t_c \propto N^{\beta(\alpha)}$, where $\beta(\alpha)$ appears to be
numerically consistent with the following behavior: $\beta >0$ for $0 \le
\alpha < 1$, and zero for $\alpha\ge 1$. 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 $\alpha$-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

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

- …