Thermodynamics of deterministic finite automata operating locally and periodically

Thomas E. Ouldridge; David H. Wolpert

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arXiv · 2208.06895

Thermodynamics of deterministic finite automata operating locally and periodically

Thomas E. Ouldridge·David H. Wolpert

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Abstract

Real-world computers have operational constraints that cause nonzero entropy production (EP). In particular, almost all real-world computers are ``periodic'', iteratively undergoing the same physical process; and ``local", in that subsystems evolve whilst physically decoupled from the rest of the computer. These constraints are so universal because decomposing a complex computation into small, iterative calculations is what makes computers so powerful. We first derive the nonzero EP caused by the locality and periodicity constraints for deterministic finite automata (DFA), a foundational system of computer science theory. We then relate this minimal EP to the computational characteristics of the DFA. We thus divide the languages recognised by DFA into two classes: those that can be recognised with zero EP, and those that necessarily have non-zero EP. We also demonstrate the thermodynamic advantages of implementing a DFA with a physical process that is agnostic about the inputs that it processes.

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Thomas E. Ouldridge, David H. Wolpert. 2022-08-14. Thermodynamics of deterministic finite automata operating locally and periodically. https://arxiv.org/abs/2208.06895

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