Thermodynamics of deterministic finite automata operating locally and periodically

TL;DR

This paper investigates the thermodynamic costs, specifically entropy production, of deterministic finite automata operating under local and periodic constraints, revealing a fundamental link between these costs and the computational properties of the automata.

Contribution

It derives the minimal entropy production for DFA under locality and periodicity constraints and classifies languages based on whether they can be recognized with zero entropy production.

Findings

DFA with certain properties can operate with zero entropy production.

Most real-world DFA inherently produce non-zero entropy due to physical constraints.

Input-agnostic DFA implementations have thermodynamic advantages.

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.