Decision Making in the Arrow of Time

Area of Science:

• Statistical mechanics
• Non-equilibrium thermodynamics
• Information theory

Background:

• Understanding the direction of time's arrow is crucial in non-equilibrium systems.
• Entropy production quantifies irreversibility in stochastic processes.

Purpose of the Study:

• To establish a quantitative relationship between entropy production and the time required to determine the arrow of time.
• To develop optimal methods for deciding the direction of time's arrow in stationary Markov processes.

Main Methods:

• Application of Wald's sequential probability ratio test for optimal decision-making.
• Utilizing mean first-passage times to estimate entropy production rates.
• Derivation of a first-passage time fluctuation theorem.

Main Results:

• Demonstrated inverse proportionality between steady-state entropy production rate and minimal decision time for time's arrow.
• Showed that entropy production can be estimated via mean first-passage times.
• Derived a fluctuation theorem where decision time distributions for correct and incorrect decisions are identical.

Conclusions:

• The study provides a novel link between thermodynamics and information theory in the context of time's arrow.
• Optimal decision strategies can efficiently determine the direction of time in stochastic systems.
• The findings are validated through numerical simulations of non-equilibrium processes.