Operational derivation of Boltzmann distribution with Maxwell's demon model

Area of Science:

• Thermodynamics
• Information Theory
• Statistical Mechanics
• Computer Science

Background:

• The Maxwell's demon paradox historically connected thermodynamics and information theory via the information erasure principle.
• Understanding the fundamental links between information processing and physical laws is crucial for statistical mechanics.

Purpose of the Study:

• To explore the foundations of statistical mechanics by modeling a "demon" with a Turing machine.
• To derive key results in statistical mechanics operationally, without relying on the principle of maximum entropy.
• To extend the model to non-equilibrium processes and demonstrate its applicability.

Main Methods:

• Utilizing a theoretical model of a Maxwell's demon equipped with a Turing machine (memory tape and processor).
• Applying operational derivation methods to statistical mechanics principles.
• Analyzing both equilibrium and non-equilibrium thermodynamic processes.

Main Results:

• An operational derivation of the Boltzmann distribution in equilibrium was achieved without postulating the maximum entropy principle.
• The dissipation-fluctuation relation was demonstrated, showcasing the model's capability for non-equilibrium analysis.

Conclusions:

• The Turing machine model provides a robust framework for understanding the interplay between information and thermodynamics.
• This approach offers a novel, operational pathway to derive fundamental concepts in statistical mechanics.
• The model's applicability to non-equilibrium systems opens avenues for further research in fluctuation theorems and related phenomena.