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The minimal work cost of information processing.

Philippe Faist¹, Frédéric Dupuis², Jonathan Oppenheim³

¹Institute for Theoretical Physics, ETH Zurich, Wolfgang-Pauli-Str. 27, Zurich 8093, Switzerland.

Nature Communications

|July 8, 2015

Summary

Landauer's principle states irreversible computation requires work. This study determines the minimal work for any logical process, linking thermodynamic and information entropy for practical applications.

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Area of Science:

Thermodynamics
Information Theory
Computational Science

Background:

Irreversible information processing incurs thermodynamic work costs, a limitation known as Landauer's principle.
Energy dissipation in computing devices hinders performance advancements, increasing the relevance of fundamental work cost principles.

Purpose of the Study:

To determine the minimal thermodynamic work required for any logical process, including computation.
To establish a precise, operational connection between thermodynamic and information entropy.

Main Methods:

Derivation of a formula for minimal work cost based on conditional entropy of discarded information.
Inclusion of statistically fluctuating work requirements in the calculation.
Application of the formula to practical scenarios like computational circuits and quantum measurements.

Main Results:

The minimal work cost for irreversible information processing is defined by the conditional entropy of discarded information relative to the computation's output.
A method is provided for explicit calculation in practical computational and quantum measurement scenarios.
A clear link is established between thermodynamic entropy and information entropy.

Conclusions:

The derived formula precisely quantifies the work cost of logical processes, accounting for fluctuations.
The findings provide a foundational understanding of the relationship between thermodynamics and information, explaining entropy's emergence in macroscopic systems.