Operational derivation of Boltzmann distribution with Maxwell’s demon model
Akio Hosoya, Koji Maruyama, Yutaka Shikano
TL;DR
This paper uses a model of Maxwell's demon to derive the Boltzmann distribution in equilibrium and explore non-equilibrium processes in statistical mechanics.
Contribution
A novel operational derivation of the Boltzmann distribution without assuming maximum entropy, using a computational demon model.
Findings
The Boltzmann distribution in equilibrium is derived operationally using a Turing-machine demon model.
The model demonstrates the dissipation-fluctuation relation for non-equilibrium processes.
The approach avoids assuming the principle of maximum entropy.
Abstract
The resolution of the Maxwell’s demon paradox linked thermodynamics with information theory through information erasure principle. By considering a demon endowed with a Turing-machine consisting of a memory tape and a processor, we attempt to explore the link towards the foundations of statistical mechanics and to derive results therein in an operational manner. Here, we present a derivation of the Boltzmann distribution in equilibrium as an example, without hypothesizing the principle of maximum entropy. Further, since the model can be applied to non-equilibrium processes, in principle, we demonstrate the dissipation-fluctuation relation to show the possibility in this direction.
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Taxonomy
TopicsAdvanced Thermodynamics and Statistical Mechanics · Statistical Mechanics and Entropy · Complex Systems and Dynamics