  Aggregators have emerged as crucial tools for the coordination of
distributed, controllable loads. However, to be used effectively, aggregators
must be able to communicate the available flexibility of the loads they control
to the system operator in a manner that is both (i) concise enough to be
scalable to aggregators governing hundreds or even thousands of loads and (ii)
informative enough to allow the system operator to send control signals to the
aggregator that lead to optimization of system-level objectives, such as cost
minimization, and do not violate private constraints of the loads, such as
satisfying specific load demands. In this paper, we present the design of a
real-time flexibility feedback signal based on maximization of entropy. The
design provides a concise and informative signal that can be used by the system
operator to perform online cost minimization and real-time capacity estimation,
while provably satisfying the private constraints of the loads. In addition to
deriving analytic properties of the design, we illustrate the effectiveness of
the design using a dataset from an adaptive electric vehicle charging network.
