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Related Concept Videos

Thermodynamic Potentials01:26

Thermodynamic Potentials

Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...
Le Chatelier's Principle: Changing Temperature02:19

Le Chatelier's Principle: Changing Temperature

Consistent with the law of mass action, an equilibrium stressed by a change in concentration will shift to re-establish equilibrium without any change in the value of the equilibrium constant, K. When an equilibrium shifts in response to a temperature change, however, it is re-established with a different relative composition that exhibits a different value for the equilibrium constant.
To understand this phenomenon, consider the elementary reaction:
Thermal Sigmatropic Reactions: Overview01:16

Thermal Sigmatropic Reactions: Overview

Sigmatropic rearrangements are a class of pericyclic reactions in which a σ bond migrates from one part of a π system to another. These are intramolecular rearrangements where the total number of σ and π bonds remain unchanged.
Sigmatropic shifts are classified based on an order term [i, j ], where i and j indicate the number of atoms across which each end of the σ bond migrates. Below are examples of a [3,3] sigmatropic shift in 1,5-hexadiene, referred to as...
Path Between Thermodynamics States01:21

Path Between Thermodynamics States

Consider the two thermodynamic processes involving an ideal gas that are represented by paths AC and ABC in Figure 1:
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
Thermodynamics: Chemical Potential and Activity01:10

Thermodynamics: Chemical Potential and Activity

The effective concentration of a species in a solution can be expressed precisely in terms of its activity. Activity considers the effect of electrolytes present in the vicinity of the species of interest and depends on the ionic strength of the solution. The activity of a species is expressed as the product of molar concentration and the activity coefficient of the species.
The thermodynamic equilibrium constant is more accurately defined in terms of activity rather than concentration.

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Related Experiment Video

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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

Two-temperature Langevin dynamics in a parabolic potential.

Victor Dotsenko1, Anna Maciołek, Oleg Vasilyev

  • 1Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600), Université Pierre et Marie Curie (Paris 6), 4 Place Jussieu, 75252 Paris, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 16, 2013
PubMed
Summary

This study explores Brownian motion with different temperatures in X and Y directions, revealing a unique particle distribution in a nonequilibrium stationary state. Theoretical findings are validated through numerical simulations.

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Published on: January 25, 2020

Area of Science:

  • Statistical Physics
  • Nonlinear Dynamics
  • Computational Physics

Background:

  • Brownian motion is fundamental to understanding particle dynamics.
  • Nonequilibrium systems exhibit complex behaviors not seen in equilibrium.
  • Anisotropic diffusion requires specialized theoretical treatment.

Purpose of the Study:

  • To investigate a planar Brownian particle diffusion under two distinct effective temperatures.
  • To determine the stationary particle position distribution in this anisotropic system.
  • To characterize the emergent nonequilibrium stationary state and its associated particle currents.

Main Methods:

  • Formulation of Langevin equations with direction-dependent effective temperatures.
  • Analytical derivation of the nontrivial stationary particle position distribution P(x,y).
  • Numerical simulations to validate theoretical predictions.

Main Results:

  • Explicit determination of the particle position distribution P(x,y).
  • Identification of a nonequilibrium stationary state.
  • Observation of space-dependent particle currents with a nonzero rotor.

Conclusions:

  • The two-temperature diffusion model leads to a unique nonequilibrium state.
  • Anisotropic diffusion can induce complex current behaviors.
  • Numerical simulations confirm the theoretical framework and findings.