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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.
PNAS Nexus
|April 24, 2026
Summary
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.
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.
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