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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Published on: December 4, 2017

Teaching the principles of statistical dynamics.

Kingshuk Ghosh1, Ken A Dill, Mandar M Inamdar

  • 1Department of Biophysics, University of California, San Francisco, California 94143.

American Journal of Physics
|April 16, 2013
PubMed
Summary
This summary is machine-generated.

We introduce a framework using maximum caliber to derive transport laws like diffusion and heat flow. This principle explains dynamical laws by analyzing microtrajectory probabilities, aligning with new single-molecule experiment capabilities.

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Area of Science:

  • Statistical mechanics
  • Physical chemistry
  • Transport phenomena

Background:

  • Classical transport laws (Fick's, Fourier's, Newtonian viscosity, mass-action) describe macroscopic phenomena.
  • Statistical mechanics traditionally uses entropy maximization for equilibrium properties.
  • Recent advances in single-particle experiments allow direct observation of dynamic trajectories.

Purpose of the Study:

  • To present a unified framework for deriving fundamental dynamical transport laws.
  • To demonstrate the principle of maximum caliber as a tool for understanding non-equilibrium dynamics.
  • To connect theoretical principles with emerging experimental capabilities in statistical dynamics.

Main Methods:

  • Applying the principle of maximum caliber to microtrajectories.
  • Drawing an analogy with entropy maximization for equilibrium statistical mechanics.
  • Deriving dynamical distribution functions for microtrajectory probabilities.

Main Results:

  • The maximum caliber principle successfully derives Fick's law of diffusion, Fourier's law of heat flow, the Newtonian viscosity law, and mass-action laws.
  • The framework yields dynamical distribution functions characterizing microtrajectory probabilities.
  • This approach provides a theoretical basis for understanding observed single-particle dynamics.

Conclusions:

  • Maximum caliber offers a powerful and unified approach to teaching and understanding dynamical transport laws.
  • The principle bridges equilibrium and non-equilibrium statistical mechanics.
  • This framework is relevant for interpreting data from advanced single-molecule and single-particle experiments.