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When a fluid encounters a solid surface, a boundary layer forms due to the interaction between the fluid's motion and the stationary surface. This phenomenon is characterized by a thin region adjacent to the surface where viscous forces dominate, influencing the fluid's velocity profile. The development of the boundary layer begins at the leading edge of the surface and evolves as the fluid moves downstream.As the fluid flows over the surface, friction between the fluid and the wall slows down...
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Boundary layers in stochastic thermodynamics.

Erik Aurell1, Carlos Mejía-Monasterio, Paolo Muratore-Ginanneschi

  • 1ACCESS Linnaeus Centre, KTH, Stockholm, Sweden and Department of Computational Biology, AlbaNova University Centre, S-106 91 Stockholm, Sweden. eaurell@kth.se

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 3, 2012
PubMed
Summary
This summary is machine-generated.

We regularized singular solutions in stochastic thermodynamics, transforming protocol jumps into finite boundary layers. This reveals that vanishing boundary layers dissipate no heat, allowing work to be done, and links optimal protocols to deterministic transport.

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Area of Science:

  • Stochastic Thermodynamics
  • Non-equilibrium Statistical Mechanics
  • Mathematical Physics

Background:

  • Optimizing heat release or work dissipation in stochastic systems is crucial.
  • Overdamped systems exhibit singular solutions, interpreted as instantaneous protocol jumps.
  • Existing models lack a mechanism to resolve these singularities physically.

Purpose of the Study:

  • To investigate the physical nature of singular solutions in stochastic thermodynamics.
  • To develop a regularization method for optimizing protocols in overdamped systems.
  • To provide an alternative interpretation of optimal protocols in terms of deterministic transport.

Main Methods:

  • Regularization of thermodynamic functionals by penalizing acceleration.
  • Analysis of boundary layer behavior in the limit of vanishing width.
  • Connection to optimal deterministic transport and Burgers' equation.

Main Results:

  • Singular protocol jumps are resolved into finite-width boundary layers.
  • In the limit of vanishing boundary layer width, no heat is dissipated.
  • Work can be performed within these boundary layers.
  • Optimal protocols in the overdamped limit correspond to optimal deterministic transport.

Conclusions:

  • The regularization approach provides a physically meaningful interpretation of optimal protocols.
  • Boundary layers represent a key feature in understanding energy dissipation and work extraction in stochastic systems.
  • The connection to Burgers' equation offers new insights into the mathematical structure of optimal stochastic control.