  The thermodynamic uncertainty relation sets the minimal bound of the
cost-precision trade-off relation for dissipative processes. Examining the
dynamics of an internally coupled system that is driven by a constant
thermodynamic force, we however find that the trade-off relation of a
sub-system is not constrained by the minimal bound of conventional uncertainty
relation. We made our point explicit by using an exactly solvable model of
interacting oscillators. As the number (N) of interacting oscillators
increases, the uncertainty bound of individual oscillators is reduced to 2k_B
T/N upon full synchronization under strong coupling. The cost-precision
trade-off for the sub-system is particularly relevant for sub-cellular
processes where collective dynamics emerges from multiple energy-expending
components interacting with each other.
