A thermodynamically consistent model of finite-state machines

Area of Science:

• Theoretical computer science
• Statistical mechanics
• Information theory

Background:

• Finite-state machines (FSMs) are fundamental computational models with broad applications.
• Understanding the physical resource requirements of computation is crucial for developing efficient computing systems.

Purpose of the Study:

• To propose a general, thermodynamically consistent model for finite-state machines (FSMs).
• To characterize the resource requirements, including entropy production and error probability, of these machines.
• To establish a theoretical framework for analyzing the physical limits of FSM computation.

Main Methods:

• Modeling FSMs as time-inhomogeneous Markov chains.
• Analyzing computation as driven by instantaneous manipulations of state energy levels.
• Calculating key thermodynamic quantities: entropy production, error probability, and update time.

Main Results:

• A general, thermodynamically consistent model for FSMs was developed.
• Resource requirements such as entropy production and error probability were quantitatively characterized.
• It was demonstrated that generalized bit-setting operations are sufficient for implementing any FSM.

Conclusions:

• The proposed model provides a rigorous framework for understanding the physical resource costs of FSMs.
• The findings offer insights into the fundamental limits and trade-offs in computational processes.
• Generalized bit-setting operations offer a universal mechanism for FSM implementation within this thermodynamic model.