Improving the Cramér-Rao bound with the detailed fluctuation theorem

Area of Science:

• Statistical Mechanics
• Non-equilibrium Thermodynamics
• Quantum Information Theory

Background:

• Entropy production is a key indicator of irreversibility in thermodynamic systems.
• The detailed fluctuation theorem (DFT) describes the statistical properties of entropy production.
• The Cramér-Rao (CR) bound provides a general limit on the precision of parameter estimation, including entropy production rates.

Purpose of the Study:

• To derive a novel upper bound for the mean entropy production rate.
• To improve upon the existing Cramér-Rao (CR) bound using the detailed fluctuation theorem (DFT).
• To validate the new bound's accuracy and saturation in specific physical systems.

Main Methods:

• Employing the detailed fluctuation theorem (DFT) to establish a new theoretical bound.
• Analyzing the time-dependent distribution of entropy production (Σ).
• Investigating heat exchange problems mediated by bosonic modes and qubits.

Main Results:

• A new upper bound for the mean entropy production rate was derived, surpassing the CR bound.
• The derived bound serves as an accurate approximation for entropy production in heat exchange via bosonic modes.
• The bound is shown to be saturated in heat exchange mediated by a weakly coupled qubit.

Conclusions:

• The detailed fluctuation theorem (DFT) offers a powerful tool for refining bounds on thermodynamic quantities.
• The newly derived bound provides a more precise estimation of entropy production rates in non-equilibrium systems.
• This work has implications for understanding and quantifying irreversibility in quantum and thermal processes.