  We explore the electronic entropy per particle $s$ and Seebeck coefficient
$\mathcal{S}$ in zigzag graphene ribbons. Pristine and edge-doped ribbons are
considered using tight-binding models to inspect the role of edge states in the
observed thermal transport properties. As a bandgap opens when the ribbons are
doped at one or both edges, due to asymmetric edge potentials, we find that $s$
and $\mathcal{S}$ signals are closely related to each other: both develop sharp
dip-peak lineshapes as the chemical potential lies in the gap, while the ratio
$s/\mathcal{S}$ exhibits a near constant value equal to the elementary charge
$e$ at low temperatures. This constant ratio suggests that $\mathcal{S}$ can be
seen as the transport differential entropy per charge, as suggested by some
authors. Our calculations also indicate that measurement of $s$ and
$\mathcal{S}$ may be useful as a spectroscopic probe of different electronic
energy scales involved in such quantities in gapped materials.
