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Local entropy production rate of run-and-tumble particles
Matteo Paoluzzi1, Andrea Puglisi2,3, Luca Angelani2
1Sapienza Università di Roma, Dipartimento di Fisica, Piazzale A. Moro 2, I-00185 Rome, Italy.
Physical Review. E
|December 23, 2025
Summary
This study analyzes entropy production and flow in active systems of run-and-tumble particles. In a stationary state, these entropies equalize, depending solely on particle distribution and spatial derivatives.
Area of Science:
- Statistical Mechanics
- Soft Matter Physics
- Active Matter Physics
Background:
- Active systems, such as biological cells or synthetic micro-machines, exhibit complex behaviors driven by internal energy consumption.
- Understanding entropy dynamics is crucial for characterizing the thermodynamics of non-equilibrium systems.
- Run-and-tumble particles provide a fundamental model for active matter, exhibiting intermittent motion.
Purpose of the Study:
- To investigate the local entropy production rate and local entropy flow in systems of noninteracting run-and-tumble particles.
- To derive general expressions for these quantities and analyze their behavior in the stationary regime.
- To explore specific scenarios including space-dependent particle speeds and external force fields.
Main Methods:
- Derivation of generic time-dependent expressions for local entropy production and flow.
- Focus on the stationary regime, simplifying the analysis to depend on distribution functions and spatial derivatives.
- Analytical treatment of specific cases: space-dependent speeds (photokinetic bacteria) and external potentials (harmonic, linear).
- Comparison of analytical results (exact and approximated) with numerical simulations.
Main Results:
- Established that in the stationary regime, local entropy production and flow are equal.
- Demonstrated that these equal entropies depend only on the distribution function and its spatial derivatives.
- Analyzed photokinetic bacteria with piecewise constant and sinusoidal speed profiles.
- Investigated systems with harmonic and linear external potentials.
Conclusions:
- The study provides a theoretical framework for understanding entropy in active matter systems.
- The equalization of entropy production and flow in the stationary state offers a significant simplification.
- The findings are validated across diverse scenarios, including biological and physically modeled systems, highlighting the robustness of the theoretical approach.
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