Exact, complete expressions for the thermodynamic costs of circuits

06/11/2018
by   David Hilton Wolpert, et al.
0

Common engineered systems implement computations using circuits, as do many biological systems (e.g., gene regulatory networks). The topology of such circuits introduces constraints on the physical system implementing the circuit. Here we derive the addition to the minimal heat flow out of a system that implements a desired computation using a given circuit rather than using an idealized system that has no constraints. We call this additional minimal heat flow "circuit Landauer loss". We show that in general different circuits computing the same function have different circuit Landauer loss. This leads to a novel optimization problem, of how to design a circuit to compute a given function with minimal circuit Landauer loss. We also analyze a second contribution to the actual heat that flows out of a circuit when running, beyond the minimum possible. We call this "circuit mismatch loss". It is the extra heat that is dissipated when a physical circuit that is designed to dissipate least heat when it is run with a distribution q over its inputs, is instead run with a distribution p q over its inputs. Circuit mismatch loss can be either positive or negative. Indeed, we show that the sum of circuit Landauer loss and circuit mismatch loss can be negative. So in practice, using a circuit to compute a function, rather than a fixed "idealized system" that has no constraints, can actually reduce the total heat produced.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

09/21/2021

On the Hardness of the Determinant: Sum of Regular Set-Multilinear Circuits

In this paper, we study the computational complexity of the commutative ...
08/19/2019

Ternary circuits: why R=3 is not the Optimal Radix for Computation

A demonstration that e=2.718 rounded to 3 is the best radix for computat...
06/15/2020

The PSPACE-hardness of understanding neural circuits

In neuroscience, an important aspect of understanding the function of a ...
11/12/2020

Thermoformed Circuit Boards: Fabrication of highly conductive freeform 3D printed circuit boards with heat bending

Fabricating 3D printed electronics using desktop printers has become mor...
12/21/2012

In Vivo Quantification of Clot Formation in Extracorporeal Circuits

Clot formation is a common complication in extracorporeal circuits. In t...
10/05/2015

Implications of Burn-In Stress on NBTI Degradation

Burn-in is accepted as a way to evaluate ageing effects in an accelerate...
03/01/2012

The Mind Grows Circuits

There is a vast supply of prior art that study models for mental process...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.