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Minimal energy cost to initialize a bit with tolerable error.

Yu-Han Ma1, Jin-Fu Chen1,2,3, C P Sun1,2

  • 1Graduate School of China Academy of Engineering Physics, No. 10 Xibeiwang East Road, Haidian District, Beijing, 100193, China.

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This study reveals the energy cost increase for finite-time bit initialization, exceeding Landauer's limit. An optimal protocol minimizes this cost for practical computing applications.

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Area of Science:

  • Thermodynamics
  • Information Theory
  • Computational Physics

Background:

  • Landauer's principle defines the theoretical minimum energy cost for erasing information.
  • Practical systems face constraints of finite operation time, deviating from ideal conditions.

Purpose of the Study:

  • To quantify the energy cost of initializing a classical bit within a finite operation time.
  • To investigate the relationship between error probability and energy cost.
  • To propose an optimal protocol for energy-efficient bit initialization.

Main Methods:

  • Theoretical analysis of energy cost in finite-time thermodynamic processes.
  • Derivation of the energy cost formula including thermodynamic length and error probability.
  • Development of an optimal protocol for isothermal bit initialization.

Main Results:

  • A new formula for energy cost is derived: Landauer's limit + L²(ε)/τ.
  • Energy cost increases with decreasing error probability (ε) and finite time (τ).
  • Specific minimal additional costs are calculated for given error probabilities and dissipation coefficients.

Conclusions:

  • Finite-time operation significantly impacts the energy cost of bit initialization.
  • The derived formula and optimal protocol offer insights into energy-efficient information processing.
  • This research bridges theoretical limits and practical constraints in computing thermodynamics.