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Conservation of Energy in Control Volume01:14

Conservation of Energy in Control Volume

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Thermodynamic Systems01:06

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Path Between Thermodynamics States

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Thermodynamic Processes01:25

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Related Experiment Video

Updated: May 16, 2026

Temperature-Controlled Assembly and Characterization of a Droplet Interface Bilayer
10:11

Temperature-Controlled Assembly and Characterization of a Droplet Interface Bilayer

Published on: April 19, 2021

Geometry of thermodynamic control.

Patrick R Zulkowski1, David A Sivak, Gavin E Crooks

  • 1Department of Physics, University of California, Berkeley, California 94720, USA. pzulkowski@berkeley.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2012
PubMed
Summary
This summary is machine-generated.

Understanding nonequilibrium phenomena is key for molecular machines. This study reveals optimal protocols for driven systems, using Riemannian geometry to find minimal-dissipation paths and a natural friction tensor derivation.

Related Experiment Videos

Last Updated: May 16, 2026

Temperature-Controlled Assembly and Characterization of a Droplet Interface Bilayer
10:11

Temperature-Controlled Assembly and Characterization of a Droplet Interface Bilayer

Published on: April 19, 2021

Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Physical Chemistry

Background:

  • Understanding nonequilibrium phenomena is crucial for molecular machines.
  • Thermodynamic systems driven from equilibrium exhibit Riemannian geometry in their controllable parameters, induced by a generalized friction tensor.
  • This geometric insight offers a novel perspective on system dynamics.

Purpose of the Study:

  • To construct closed-form expressions for minimal-dissipation protocols.
  • To explore the geometric properties of controllable parameters in driven thermodynamic systems.
  • To derive the friction tensor without direct reliance on linear response theory.

Main Methods:

  • Exploiting Riemannian geometry of controllable parameters.
  • Constructing geodesics on the relevant manifold for optimal protocols.
  • Numerical implementation of the Fokker-Planck equation to test protocols.
  • Analyzing the emergence of the friction tensor from parameter derivatives.

Main Results:

  • Closed-form expressions for minimal-dissipation protocols were derived for a diffusing particle in a harmonic potential.
  • Optimal protocols correspond to geodesics on the Riemannian manifold, revealing rich geometry in a simple model.
  • The friction tensor naturally arises from a first-order expansion of temporal parameter derivatives.

Conclusions:

  • The geometric framework provides a powerful tool for understanding and designing protocols for nonequilibrium systems.
  • This approach simplifies the derivation of the friction tensor, offering new insights into its origins.
  • The findings have implications for the design and control of natural and synthetic molecular machines.