The primary objective of this study is to explore the connection of the device physics in the Boltzmann-Heisenberg limits and the parameters of the digital circuits implemented from these devices. We offer an abstraction of a Minimal Turing Machine built from the limiting devices and circuits, thus Turing-Heisenberg Rapprochement. The analysis suggests a possible limit to computational performance similar to the Carnot efficiency limit for heat engines. (c) 2010 Elsevier Ltd. All rights reserved.