Thermodynamics of Random Number Generation

TL;DR

This paper examines the thermodynamic costs of different random number generation methods, revealing fundamental bounds on energy use and dissipation, and highlighting the unique capabilities of true random number generators in energy conversion.

Contribution

It provides a comprehensive thermodynamic analysis of RNG algorithms, establishing bounds on heat and work, and introduces a new thermodynamic model for true random number generators.

Findings

TRNGs can convert thermal energy into stored work.

Different RNG methods have distinct thermodynamic costs.

Bounds on heat dissipation and work are established for various algorithms.

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.