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Thermodynamics of Random Number Generation
Statistical Mechanics · Submitted 26 Dec 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The results highlight the significant differences between the three main approaches to random number generation: One is work producing, one is work consuming, and the other is potentially dissipation neutral.
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The abstract, sentence by sentence
We analyze the thermodynamic costs of the three main approaches to generating random numbers via the recently introduced Information Processing Second Law. Given access to a specified source of randomness, a random number generator (RNG) produces samples from a desired target probability distribution. This differs from pseudorandom number generators (PRNG) that use wholly deterministic algorithms and from true random number generators (TRNG) in which the randomness source is a physical system. For each class, we analyze the thermodynamics of generators based on algorithms implemented as finite-state machines, as these allow for direct bounds on the required physical resources. This establishes bounds on heat dissipation and work consumption during the operation of three main classes of RNG algorithms---including those of von Neumann, Knuth and Yao, and Roche and Hoshi---and for PRNG methods. We introduce a general TRNG and determine its thermodynamic costs exactly for arbitrary target distributions. The results highlight the significant differences between the three main approaches to random number generation: One is work producing, one is work consuming, and the other is potentially dissipation neutral. Notably, TRNGs can both generate random numbers and convert thermal energy to stored work. These thermodynamic costs on information creation complement Landauer's limit on the irreducible costs of information destruction.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We analyze the thermodynamic costs of the three main approaches to generating random numbers via the recently introduced Information Processing Second Law. | contribution 1.00 | 0.92 | 0.10 | asserted 0.95 |
| s1 | Given access to a specified source of randomness, a random number generator (RNG) produces samples from a desired target probability distribution. | background 1.00 | 0.07 | 0.03 | asserted 1.00 |
| s2 | This differs from pseudorandom number generators (PRNG) that use wholly deterministic algorithms and from true random number generators (TRNG) in which the randomness source is a physical system. | background 1.00 | 0.06 | 0.02 | asserted 1.00 |
| s3 | For each class, we analyze the thermodynamics of generators based on algorithms implemented as finite-state machines, as these allow for direct bounds on the required physical resources. | method 0.96 | 0.69 | 0.03 | asserted 0.96 |
| s4 | This establishes bounds on heat dissipation and work consumption during the operation of three main classes of RNG algorithms---including those of von Neumann, Knuth and Yao, and Roche and Hoshi---and for PRNG methods. | result 0.71 | 0.85 | 0.15 | asserted 1.00 |
| s5 | We introduce a general TRNG and determine its thermodynamic costs exactly for arbitrary target distributions. | contribution 0.97 | 0.95 | 0.11 | asserted 1.00 |
| s6 | The results highlight the significant differences between the three main approaches to random number generation: One is work producing, one is work consuming, and the other is potentially dissipation neutral. | interpretation 0.51 | 0.87 | 0.67 | asserted 0.92 |
| s7 | Notably, TRNGs can both generate random numbers and convert thermal energy to stored work. | result 0.88 | 0.81 | 0.23 | asserted 0.69 |
| s8 | These thermodynamic costs on information creation complement Landauer's limit on the irreducible costs of information destruction. | interpretation 0.95 | 0.45 | 0.13 | asserted 0.98 |
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Original abstract
We analyze the thermodynamic costs of the three main approaches to generating random numbers via the recently introduced Information Processing Second Law. Given access to a specified source of randomness, a random number generator (RNG) produces samples from a desired target probability distribution. This differs from pseudorandom number generators (PRNG) that use wholly deterministic algorithms and from true random number generators (TRNG) in which the randomness source is a physical system. For each class, we analyze the thermodynamics of generators based on algorithms implemented as finite-state machines, as these allow for direct bounds on the required physical resources. This establishes bounds on heat dissipation and work consumption during the operation of three main classes of RNG algorithms---including those of von Neumann, Knuth and Yao, and Roche and Hoshi---and for PRNG methods. We introduce a general TRNG and determine its thermodynamic costs exactly for arbitrary target distributions. The results highlight the significant differences between the three main approaches to random number generation: One is work producing, one is work consuming, and the other is potentially dissipation neutral. Notably, TRNGs can both generate random numbers and convert thermal energy to stored work. These thermodynamic costs on information creation complement Landauer's limit on the irreducible costs of information destruction.
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Cites as background 2 papers
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More sophisticated random stochastic process generators employing quantum physics have been introduced recently [ref] .
The Ambiguity of Simplicity · True Random Number Generation · 0.83
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More sophisticated random stochastic process generators employing quantum physics have been introduced recently [ref] .
Extreme Quantum Advantage when Simulating Strongly Coupled Classical Systems · True Random Number Generation · 0.83
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