The physical limit of logical compare operation

TL;DR

This paper demonstrates that the physical and logical complexity of compare operations is fundamentally limited by thermodynamics, establishing a lower bound on sorting time complexity and linking information theory with thermodynamics.

Contribution

It introduces a thermodynamic model using Szilard engines to analyze compare operations and proves a fundamental physical limit on their complexity.

Findings

Compare operation complexity is kTln2 thermodynamic cost.

Lower bound on sorting time complexity is established.

Confirms the equivalence between information entropy and thermodynamic entropy.

Abstract

In this paper two connected Szilard single molecule engines (with different temperature) model of Maxwell's demon are used to demonstrate and analysis the logical compare operation. The logical and physical complexity of compare operations are both showed to be kTln2. Then this limit was used to prove the time complexity lower bound of sorting problem. It confirmed the proposed way to measure the complexity of a problem, provided another evidence of the equivalence between information theoretical and thermodynamic entropies.