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Entropy production bounds for systems running computer programs.

Abhishek Yadav1,2, Francesco Caravelli3, David Wolpert1,4,5,6

  • 1Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA.

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Summary
This summary is machine-generated.

Mismatch cost (MMC), a lower bound on entropy production (EP), scales linearly with heat flow. This study introduces a framework to compute MMC for computer programs, analyzing sorting algorithms and subroutine calls.

Keywords:
computer programsentropy productionmismatch costnonequilibrium thermodynamicsthermodynamic cost of computation

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Area of Science:

  • Thermodynamics
  • Computer Science
  • Information Theory

Background:

  • Entropy production (EP) quantifies irreversibility in physical processes.
  • Mismatch cost (MMC) provides a universal lower bound for EP over a time interval.
  • Understanding the thermodynamic cost of computation is crucial for efficient computing.

Purpose of the Study:

  • Establish theoretical results for mismatch cost (MMC) and its scaling with heat flow.
  • Develop a general framework for computing the minimal EP (MMC) of computational processes.
  • Analyze the thermodynamic cost of sorting algorithms using the developed framework.

Main Methods:

  • Deriving theoretical bounds for mismatch cost (MMC) related to heat flow.
  • Introducing a general computational framework to calculate minimal entropy production (MMC).
  • Applying the framework to compare bubble sort and bucket sort, considering input size and structure.

Main Results:

  • Proved MMC scales at least linearly with total heat flow in the worst case.
  • Demonstrated that subdividing time intervals does not decrease the MMC lower bound.
  • Showcased the framework's ability to analyze thermodynamic costs influenced by input characteristics.

Conclusions:

  • MMC is a fundamental thermodynamic limit for computational processes.
  • The developed framework allows for detailed analysis of computational thermodynamic costs.
  • Insights into the efficiency of algorithms like bubble sort and bucket sort from a thermodynamic perspective.