  Recently, some general relations have been studied in nonequilibrium
mesoscopic systems. In particular, the thermodynamic uncertainty relation (TUR)
provides a universal internal relation among the cumulants of currents and the
entropy production. In this paper, we give a simple derivation of TUR for
thermally fluctuating particle current in a tilted periodic potential from a
coarse grained point of view with the use of the transition probabilities.
Also, we explore the condition for the bound of TUR to monotonically increase
with the affinity.
