  A microscopic model of interacting oscillators, which admits two conserved
quantities, volume, and energy, is investigated. We begin with a system driven
by a general nonlinear potential under high-temperature regime by taking the
inverse temperature of the system asymptotically small. As a consequence, one
can extract a principal part (by a simple Taylor expansion argument), which is
driven by the harmonic potential, and we show that previous results for the
harmonic chain are covered with generality. We consider two fluctuation fields,
which are defined as a linear combination of the fluctuation fields of the two
conserved quantities, volume, and energy, and we show that the fluctuations of
one field converge to a solution of an additive stochastic heat equation, which
corresponds to the Ornstein-Uhlenbeck process, in a weak asymmetric regime, or
to a solution of the stochastic Burgers equation, in a stronger asymmetric
regime. On the other hand, the fluctuations of the other field cross from an
additive stochastic heat equation to a fractional diffusion equation given by a
skewed L\'evy process.
