Information bound for entropy production from the detailed fluctuation theorem

Area of Science:

• Thermodynamics and Statistical Mechanics
• Information Theory
• Quantum Information

Background:

• Fluctuation theorems provide fundamental statistical bounds on entropy production, with the second law of thermodynamics being a key example.
• Understanding the information content of entropy production is crucial for exploring thermodynamic limits.

Purpose of the Study:

• To quantify the information of entropy production using information theory.
• To establish a tight upper bound for entropy production information as a function of its mean, derived from the strong detailed fluctuation theorem.

Main Methods:

• Applied information theory to quantify entropy production.
• Derived an upper bound using the strong detailed fluctuation theorem, defining a maximal distribution.
• Investigated physical systems including bosonic heat transfer, levitated nanoparticle heat transfer, and qubit swap engines.

Main Results:

• An upper tight bound for entropy production information was established, expressed by a maximal distribution.
• Entropy production in a weakly coupled bosonic heat transfer model reproduced the maximal distribution in a limiting case.
• The bound was extended to continuous domains and validated with heat transfer in a levitated nanoparticle.
• Compositions of qubit swap engines were shown to satisfy a specific case of the maximal distribution irrespective of their size.

Conclusions:

• The study successfully quantifies entropy production information and establishes a universal upper bound.
• The findings demonstrate the applicability of the derived bound across classical and quantum systems, including heat transfer and quantum engines.
• The research highlights the connection between information theory, thermodynamics, and quantum mechanics.