  For the long-range one-dimensional Ising spin-glass with random couplings
decaying as $J(r) \propto r^{-\sigma}$, the scaling of the effective coupling
defined as the difference between the free-energies corresponding to Periodic
and Antiperiodic boundary conditions $J^R(N) \equiv F^{(P)}(N)-F^{(AP)}(N) \sim
N^{\theta(\sigma)}$ defines the droplet exponent $\theta(\sigma)$. Here we
study numerically the instability of the renormalization flow of the effective
coupling $J^R(N)$ with respect to magnetic, disorder and temperature
perturbations respectively, in order to extract the corresponding chaos
exponents $\zeta_H(\sigma)$, $\zeta_J(\sigma)$ and $\zeta_T(\sigma)$ as a
function of $\sigma$. Our results for $\zeta_T(\sigma) $ are interpreted in
terms of the entropy exponent $\theta_S(\sigma) \simeq 1/3$ which governs the
scaling of the entropy difference $ S^{(P)}(N)-S^{(AP)}(N) \sim
N^{\theta_S(\sigma)}$. We also study the instability of the ground state
configuration with respect to perturbations, as measured by the spin overlap
between the unperturbed and the perturbed ground states, in order to extract
the corresponding chaos exponents $\zeta^{overlap}_H(\sigma)$ and
$\zeta^{overlap}_J(\sigma)$.
