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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
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Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If...
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Entropy Production of Run-and-Tumble Particles.

Matteo Paoluzzi1, Andrea Puglisi2,3, Luca Angelani2,3

  • 1Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche, Via Pietro Castellino 111, I-80131 Napoli, Italy.

Entropy (Basel, Switzerland)
|June 26, 2024
PubMed
Summary
This summary is machine-generated.

We analyzed entropy production in run-and-tumble models, deriving exact results for anisotropic and multi-dimensional motion using Fokker-Planck equations. This provides a framework for understanding non-equilibrium statistical mechanics in complex systems.

Keywords:
active matterentropy productionexact resultsnon-equilibriumrun-and-tumble motion

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Area of Science:

  • Statistical Mechanics
  • Non-Equilibrium Physics
  • Theoretical Biophysics

Background:

  • Run-and-tumble models are crucial for describing active matter dynamics.
  • Understanding entropy production is key to characterizing non-equilibrium processes.
  • Fokker-Planck equations provide a powerful framework for analyzing stochastic systems.

Purpose of the Study:

  • To analyze entropy production in various run-and-tumble models.
  • To derive exact results for both simple and complex scenarios.
  • To extend the analysis to anisotropic and multi-dimensional systems.

Main Methods:

  • General formalism using Fokker-Planck equations in one dimension.
  • Derivation of exact results for free and confined particles.
  • Extension to anisotropic motion with different speeds and tumbling rates.
  • Analysis of space-dependent parameters and d-dimensional motion.

Main Results:

  • Exact expressions for entropy production rate in simple and anisotropic cases.
  • Framework for analyzing heterogeneous and multi-dimensional run-and-tumble motion.
  • Validation of known results through the general formalism.

Conclusions:

  • The study provides a comprehensive framework for entropy production in run-and-tumble models.
  • Exact results are obtained for diverse physical situations, including anisotropic and d-dimensional cases.
  • The findings contribute to the understanding of non-equilibrium statistical mechanics in active matter.