Field theories of active particle systems and their entropy production

Area of Science:

• Statistical Mechanics
• Soft Matter Physics
• Theoretical Physics

Background:

• Active particles convert chemical energy into self-propulsion, creating non-equilibrium steady states.
• Entropy production quantifies the system's deviation from equilibrium and its capacity to perform work.
• Approximate field theories often fail to accurately capture microscopic dynamics, leading to errors in entropy production calculations.

Purpose of the Study:

• To develop an exact method for calculating entropy production in active matter systems.
• To demonstrate the utility of Doi-Peliti field theories for modeling microscopic particle dynamics.
• To provide a framework for deriving exact expressions for entropy production in interacting particle systems.

Main Methods:

• Utilizing Doi-Peliti field theories, which inherently account for microscopic dynamics and interactions.
• Constructing field theories from a Fokker-Planck equation (FPE).
• Calculating entropy production from first principles, capturing reactions and potentials.

Main Results:

• An exact, systematic approximation scheme using diagrammatics is established.
• General, compact, and efficient expressions for entropy production in interacting conserved particle systems are derived.
• The method reveals relationships between interaction order and density correlations (e.g., pair interactions depend on three-point density).

Conclusions:

• Doi-Peliti field theories offer an exact and systematically improvable approach to calculating entropy production in active matter.
• The derived expressions are independent of the specific field theory and applicable to experimental and numerical data.
• This work represents a paradigm shift, enabling exact entropy production calculations from microscopic dynamics.