Abstract
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 system implementing a circuit. We investigate how such restrictions on the physical coupling affects the thermodynamic costs of the circuit. To do this we first calculate the minimal additional entropy production that arises when we run a given gate in a circuit, if the physical process implementing that gate can only be coupled to variables in the rest of the circuit that feed in or out of that gate. 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.
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