The fundamental problem considered in this paper is What is the textit{energy} consumed for the implementation of a emph{compressive sensing} decoding algorithm on a circuit?. Using the information-friction framework, we examine the smallest amount o
f textit{bit-meters} as a measure for the energy consumed by a circuit. We derive a fundamental lower bound for the implementation of compressive sensing decoding algorithms on a circuit. In the setting where the number of measurements scales linearly with the sparsity and the sparsity is sub-linear with the length of the signal, we show that the textit{bit-meters} consumption for these algorithms is order-tight, i.e., it matches the lower bound asymptotically up to a constant factor. Our implementations yield interesting insights into design of energy-efficient circuits that are not captured by the notion of computational efficiency alone.
