Lower bound for entropy production rate in stochastic systems far from equilibrium

Area of Science:

• Non-equilibrium thermodynamics
• Statistical mechanics
• Graph theory

Background:

• Entropy production is a key measure in non-equilibrium systems.
• Markov graph properties can reveal insights into system dynamics.
• Existing inequalities like Pinsker's inequality provide bounds on divergence measures.

Purpose of the Study:

• To establish a lower bound for the Schnakenberg entropy production rate.
• To develop a general theorem for bounding Kullback-Leibler divergence.
• To explore connections between non-equilibrium thermodynamics and graph theory.

Main Methods:

• Analysis of master equations to define entropy production rate.
• Definition and utilization of Markov graph weight (sum of absolute probability currents).
• Development of a general theorem for bounding Kullback-Leibler divergence using total variation.

Main Results:

• A lower bound for the Schnakenberg entropy production rate is derived, dependent on Markov graph weight.
• The bound is valid for time-dependent, non-equilibrium entropy production rates.
• A novel theorem provides a tight lower bound for Kullback-Leibler divergence between a distribution and its involution-transformed counterpart, improving on Pinsker's inequality.

Conclusions:

• The study demonstrates a functional relationship between graph properties and thermodynamic quantities.
• The derived bounds offer new analytical tools for non-equilibrium systems.
• The findings highlight the interplay between statistical mechanics, graph theory, and information theory.