  Many biological functions require the dynamics to be necessarily driven
out-of-equilibrium. In contrast, in various contexts, a nonequilibrium dynamics
at fast timescales can be described by an effective equilibrium dynamics at a
slower timescale. In this work we study the two different aspects, (i) the
energy-efficiency tradeoff for a specific nonequilibrium linear dynamics of two
variables with feedback, and (ii) the cost of effective parameters in a
coarse-grained theory as given by the "hidden" dissipation and entropy
production rate in the effective equilibrium limit of the dynamics. To
meaningfully discuss the tradeoff between energy consumption and the efficiency
of the desired function, a one-to-one mapping between function(s) and energy
input is required. The function considered in this work is the variance of one
of the variables. We get a one-to-one mapping by considering the minimum
variance obtained for a fixed entropy production rate and vice-versa. We find
that this minimum achievable variance is a monotonically decreasing function of
the given entropy production rate. When there is a timescale separation, in the
effective equilibrium limit, the cost of the effective potential and
temperature is the associated "hidden" entropy production rate.
