Thermodynamic cost for precision of general counting observables

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Physical Systems

Background:

• Understanding the fundamental limits of measurement precision in physical systems is crucial.
• Existing theories like the thermodynamic uncertainty relation provide bounds for specific systems.
• Extending these bounds to broader classes of systems and observables is an active research area.

Purpose of the Study:

• To derive universal bounds on the trade-off between thermodynamic cost and precision for hidden physical systems.
• To extend these bounds to both time-symmetric and asymmetric observables in nonequilibrium driven systems.
• To investigate methods for achieving optimal precision and identify conditions for enhanced accuracy.

Main Methods:

• Analytical derivation of universal bounds.
• Quantification of precision using fluctuations in event counts and waiting times.
• Analysis of nonequilibrium driven systems, including time-symmetric and asymmetric observables.

Main Results:

• Established universal bounds describing the thermodynamic cost-precision trade-off.
• Demonstrated how to achieve optimal precision that saturates these bounds.
• Identified a phase transition in optimal configurations for asymmetric observables, enabling precision enhancement through signal combination.

Conclusions:

• The derived bounds provide a fundamental understanding of precision limits in a wide range of physical systems.
• Optimal precision strategies exist and can be achieved under specific conditions.
• Signal combination offers a pathway to overcome precision limitations for asymmetric observables.