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Thermodynamics of random number generation
Cina Aghamohammadi1, James P Crutchfield1
1Complexity Sciences Center and Department of Physics, University of California at Davis, One Shields Avenue, Davis, California 95616, USA.
Physical Review. E
|July 16, 2017
Summary
This study quantifies the thermodynamic costs of random number generators (RNGs), distinguishing between work-producing, work-consuming, and dissipation-neutral methods. True random number generators (TRNGs) can convert thermal energy into work.
Area of Science:
- Thermodynamics
- Information Theory
- Computer Science
Background:
- Random number generators (RNGs) are crucial for various computational tasks.
- Existing RNGs include pseudorandom number generators (PRNGs) and true random number generators (TRNGs).
- The Information Processing Second Law provides a framework for analyzing the physical costs of information processing.
Purpose of the Study:
- To analyze the thermodynamic costs associated with different classes of random number generators.
- To establish bounds on heat dissipation and work consumption for RNG algorithms.
- To investigate the potential for work production or consumption in various RNG approaches.
Main Methods:
- Analysis of RNG algorithms implemented as finite-state machines.
- Application of the Information Processing Second Law to quantify thermodynamic costs.
- Exact determination of thermodynamic costs for a general true random number generator (TRNG).
Main Results:
- Significant thermodynamic differences exist between work-producing, work-consuming, and dissipation-neutral RNGs.
- True random number generators (TRNGs) can simultaneously generate random numbers and convert thermal energy into stored work.
- Bounds on heat dissipation and work consumption were established for specific RNG algorithms (von Neumann, Knuth, Yao, Roche, Hoshi) and PRNGs.
Conclusions:
- Thermodynamic costs provide a fundamental understanding of the physical resources required for random number generation.
- TRNGs offer unique capabilities in energy conversion alongside random number production.
- These findings complement existing knowledge on the irreducible costs of information destruction (Landauer's limit).
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