Landauer's Principle a Consequence of Bit Flows, Given Stirling's Approximation

Area of Science:

• Thermodynamics
• Information Theory
• Statistical Mechanics

Background:

• Landauer's principle quantifies the minimum energy (k_B ln 2 * T Joules) required to erase a bit of information in a thermodynamic system at temperature T.
• Existing arguments for Landauer's principle typically rely on the equipartition principle, limiting its applicability.

Purpose of the Study:

• To explore the energy cost of information transfer and state restoration in thermodynamic systems.
• To demonstrate the validity of Landauer's principle beyond the equipartition principle's regime.
• To provide a conceptual understanding of entropy using algorithmic information theory.

Main Methods:

• Exploration of a simple thermodynamic system model.
• Application of algorithmic information theory.
• Analysis of energy allocation statistics between stored and thermal states.

Main Results:

• The energy cost for transferring or restoring a bit in a reversible system is confirmed to be k_B ln 2 * T Joules.
• Landauer's principle is shown to be a consequence of energy allocation statistics, applicable outside the equipartition principle's validity.
• Thermodynamic entropy is linked to algorithmic entropy, quantifying bit flows to maintain systems away from equilibrium.

Conclusions:

• The study provides a robust theoretical framework for Landauer's principle, grounded in algorithmic information theory.
• The findings offer a simplified conceptualization of entropy and its relation to information processing.
• The approach aligns classical and quantum versions of Landauer's principle and can derive thermodynamic properties like heat capacities.