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Finite-time adiabatic processes: Derivation and speed limit.

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Area of Science:

  • Thermodynamics and Statistical Mechanics
  • Soft Matter Physics
  • Non-equilibrium Physics

Background:

  • Achieving adiabatic processes within finite timescales is a significant challenge in mesoscopic systems.
  • Brownian particles in arbitrary potentials are relevant models for both theoretical and practical studies.

Purpose of the Study:

  • To explicitly construct finite-time adiabatic processes for an overdamped Brownian particle.
  • To investigate the role of potential and temperature engineering in these processes.
  • To identify and quantify fundamental speed limits imposed by the second law of thermodynamics.

Main Methods:

  • Engineering the time evolution of the binding potential.
  • Simultaneously controlling the fluid temperature over time.
  • Analytical derivation of the minimum time for adiabatic transformations.

Main Results:

  • A method is presented to build finite-time adiabatic processes for Brownian particles.
  • The second law of thermodynamics imposes a minimum time (speed limit) for these transformations.
  • This minimum time is explicitly calculable for compression and decompression scenarios.

Conclusions:

  • Finite-time adiabatic processes can be constructed for mesoscopic systems by jointly controlling potential and temperature.
  • The second law dictates a fundamental speed limit for connecting equilibrium states in finite time.
  • This provides a framework for understanding and optimizing non-equilibrium processes in relevant physical systems.