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Related Concept Videos

Damped Oscillations01:07

Damped Oscillations

In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...
Entropy02:39

Entropy

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
Entropy01:18

Entropy

The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
Types of Damping01:20

Types of Damping

If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...
Reynolds Transport Theorem01:24

Reynolds Transport Theorem

The Reynolds transport theorem provides a framework to relate the time rate of change of an extensive property within a system to that in a control volume, which is crucial for analyzing fluid dynamics. Extensive properties, such as mass, velocity, acceleration, temperature, and momentum, can be expressed in terms of the mass of a fluid portion. These properties are called extensive because they depend on the system's size, while intensive properties are their corresponding values per unit mass.
Second Order systems II01:18

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If  ζ...

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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

Generalized fluctuation-dissipation theorem for steady-state systems.

J Prost1, J-F Joanny, J M R Parrondo

  • 1Physicochimie Curie (CNRS-UMR168), Institut Curie, Section de Recherche, 26 rue d'Ulm ,75248 Paris, Cedex 05, France.

Physical Review Letters
|October 2, 2009
PubMed
Summary
This summary is machine-generated.

The fluctuation-dissipation theorem, key in statistical physics, can be restored in nonequilibrium systems. A modified theorem applies to systems with Markovian dynamics, revealing universal behaviors.

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Area of Science:

  • Statistical Physics
  • Non-equilibrium Dynamics
  • Dynamical Systems Theory

Background:

  • The fluctuation-dissipation theorem (FDT) is fundamental for systems in thermodynamic equilibrium.
  • Violation of the FDT indicates a system is not in equilibrium.
  • Understanding nonequilibrium systems is crucial in various scientific fields.

Purpose of the Study:

  • To demonstrate the restoration of a fluctuation-response theorem in nonequilibrium steady states.
  • To establish a generalized FDT applicable to systems with Markovian dynamics.
  • To explore the implications of this generalized theorem across different dynamical systems.

Main Methods:

  • Analysis of systems with Markovian dynamics in nonequilibrium steady states.
  • Identification of appropriate observables to restore a fluctuation-response theorem.
  • Application and illustration using linear stochastic dynamics.
  • Case studies involving molecular motors and Hopf bifurcations.

Main Results:

  • A fluctuation-response theorem, analogous to the equilibrium FDT, is restored for systems with Markovian dynamics in nonequilibrium steady states.
  • This generalized theorem holds for a wide range of dynamical systems.
  • The study provides concrete examples in stochastic dynamics, molecular motors, and Hopf bifurcations.

Conclusions:

  • The restored fluctuation-response theorem offers a powerful tool for analyzing nonequilibrium systems.
  • It highlights universal features of systems driven out of equilibrium.
  • The findings have broad implications for statistical physics and related disciplines.