A thermodynamically consistent model of finite state machines

TL;DR

This paper introduces a thermodynamically consistent model of finite state machines, analyzing their resource costs, error rates, and operational time by modeling them as energy-manipulating Markov chains.

Contribution

It presents a novel thermodynamic framework for FSMs, characterizing their resource requirements and demonstrating that generalised bit-setting operations can implement any FSM.

Findings

Entropy production and error probabilities are quantified.

FSMs can be realized through sequences of generalized bit-setting operations.

The model links thermodynamics with computational state transitions.

Abstract

Finite state machines (FSMs) are a theoretically and practically important model of computation. We propose a general, thermodynamically consistent model of FSMs and characterise the resource requirements of these machines. We model FSMs as time-inhomogeneous Markov chains. The computation is driven by instantaneous manipulations of the energy levels of the states. We calculate the entropy production of the machine, its error probability, and the time required to complete one update step. We find that a sequence of generalised bit-setting operations is sufficient to implement any FSM.