  Digital computers implement computations using circuits, as do many naturally
occurring systems (e.g., gene regulatory networks). The topology of any such
circuit restricts which variables may be physically coupled during the
operation of a circuit. We investigate how such restrictions on the physical
coupling affects the thermodynamic costs of running the circuit. To do this we
first calculate the minimal additional entropy production that arises when we
run a given gate in a circuit. We then build on this calculation, to analyze
how the thermodynamic costs of implementing a computation with a full circuit,
comprising multiple connected gates, depends on the topology of that circuit.
This analysis provides a rich new set of optimization problems that must be
addressed by any designer of a circuit, if they wish to minimize thermodynamic
costs.
