Thermodynamics of computing with circuits

TL;DR

This paper explores how circuit topology influences the thermodynamic costs of computation, calculating minimal entropy production for gates and analyzing how circuit structure impacts overall thermodynamic efficiency.

Contribution

It introduces a method to quantify thermodynamic costs based on circuit topology and provides a framework for optimizing circuit design to minimize entropy production.

Findings

Minimal entropy production for individual gates calculated.

Thermodynamic costs depend on circuit topology.

Optimization problems for thermodynamic efficiency identified.

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 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.