  The spectral evolution and spectral lag behavior of 92 bright pulses from 84
gamma-ray bursts (GRBs) observed by the Fermi GBM telescope are studied. These
pulses can be classified into hard-to-soft pulses (H2S, 64/92),
H2S-dominated-tracking pulses (21/92), and other tracking pulses (7/92). We
focus on the relationship between spectral evolution and spectral lags of H2S
and H2S-dominated-tracking pulses. %in hard-to-soft pulses (H2S, 64/92) and
H2S-dominating-tracking (21/92) pulses. The main trend of spectral evolution
(lag behavior) is estimated with $\log E_p\propto k_E\log(t+t_0)$
(${\hat{\tau}} \propto k_{\hat{\tau}}\log E$), where $E_p$ is the peak photon
energy in the radiation spectrum, $t+t_0$ is the observer time relative to the
beginning of pulse $-t_0$, and ${\hat{\tau}}$ is the spectral lag of photons
with energy $E$ with respect to the energy band $8$-$25$ keV. For H2S and
H2S-dominated-tracking pulses, a weak correlation between $k_{{\hat{\tau}}}/W$
and $k_E$ is found, where $W$ is the pulse width. We also study the spectral
lag behavior with peak time $t_{\rm p_E}$ of pulses for 30 well-shaped pulses
and estimate the main trend of the spectral lag behavior with $\log t_{\rm
p_E}\propto k_{t_p}\log E$. It is found that $k_{t_p}$ is correlated with
$k_E$. We perform simulations under a phenomenological model of spectral
evolution, and find that these correlations are reproduced. We then conclude
that spectral lags are closely related to spectral evolution within the pulse.
The most natural explanation of these observations is that the emission is from
the electrons in the same fluid unit at an emission site moving away from the
central engine, as expected in the models invoking magnetic dissipation in a
moderately-high-$\sigma$ outflow.
