Thermodynamics of deterministic finite automata operating locally and periodically
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.
- Publication:
-
New Journal of Physics
- Pub Date:
- December 2023
- DOI:
- 10.1088/1367-2630/ad1070
- arXiv:
- arXiv:2208.06895
- Bibcode:
- 2023NJPh...25l3013O
- Keywords:
-
- Thermodynamics;
- computation;
- information;
- stochastic thermodynamics;
- mismatch cost;
- deterministic finite automata;
- modularity cost;
- Condensed Matter - Statistical Mechanics