Time-Resolved Statistics of Snippets as General Framework for Model-Free Entropy Estimators

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Non-equilibrium Systems

Background:

• Irreversibility in physical systems is typically quantified using entropy production.
• Traditional methods rely on measuring time-antisymmetric observables, such as currents, to estimate entropy production.
• A limitation exists in quantifying irreversibility when only time-symmetric events are observable.

Purpose of the Study:

• To introduce a general framework for inferring lower bounds on entropy production.
• To enable estimation of entropy production using time-resolved statistics of events with any time-reversal symmetry.
• To provide an accessible method for quantifying irreversibility beyond traditional current measurements.

Main Methods:

• Developed a general framework based on time-resolved event statistics.
• Introduced a weakened definition of Markovianity applicable to specific events.
• Utilized snippets of system trajectories between Markovian events and a generalized detailed balance relation.

Main Results:

• Established a method to infer a lower bound on entropy production from any type of event statistics.
• Demonstrated that time-symmetric instantaneous events can be used for entropy production estimation.
• Provided an operationally accessible criterion for the weakened Markov property.

Conclusions:

• The proposed framework offers a versatile approach to quantifying irreversibility.
• This method expands the scope of measurable observables for entropy production estimation.
• The concept of event-specific Markovianity simplifies the analysis of complex trajectories.