Probability inequalities for direct and inverse dynamical outputs in driven fluctuating systems

Area of Science:

• Statistical Mechanics
• Non-equilibrium Thermodynamics
• Stochastic Processes

Background:

• Fluctuating systems subjected to time-dependent drives or nonconservative forces can exhibit broken direct-inverse symmetry, leading to average bias.
• The fluctuation theorem is a fundamental concept in stochastic thermodynamics for analyzing such systems.

Purpose of the Study:

• To inspect the unbalancing between direct and inverse dynamical outputs (events) in a bidirectional forward-backward setup.
• To establish mutual bounds between the probabilities of occurrence of direct and inverse events in forward and backward modes.

Main Methods:

• Utilizing the fluctuation theorem for systems in contact with a thermal bath.
• Assuming Markov dynamics on uncontrolled degrees of freedom.
• Analyzing systems under time-dependent drives and time-independent external forces.

Main Results:

• Derived mutual bounds on probabilities of direct and inverse events.
• Re-derived generalized thermodynamic uncertainty relations.
• Derived constraints on the work distribution function for systems in steady conditions.

Conclusions:

• The study provides a framework for understanding symmetry breaking and bias in fluctuating systems.
• The findings offer new insights into generalized thermodynamic uncertainty relations and work distribution functions in non-equilibrium steady states.