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Related Concept Videos

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Fast Reactions01:27

Fast Reactions

Fast reactions occurring in times shorter than the time needed to mix reactants pose a unique challenge for investigation. In a liquid-phase continuous-flow system, reactants A and B are swiftly pushed into the mixing chamber, where mixing occurs within 1 ms. The reaction mixture then flows through an observation tube, and one measures light absorption to determine species concentrations at various points of the tube. This method is most appropriate when relatively large volumes of reactants...
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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...
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Named after the French chemist Henry Louis Le Chatelier, Le Chatelier's principle states that when a system at equilibrium is subjected to any change (like pressure, temperature, or concentration), the composition of the system adjusts in a way that counteracts the effect of this change, thereby attempting to restore the equilibrium.According to Le Chatelier's principle, for exothermic reactions, when the system's temperature is increased, the system will try to reduce the temperature. This...

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Probing nonequilibrium fluctuations through linear response.

Takahiro Sakaue1, Takao Ohta

  • 1Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan. sakaue@scphys.kyoto-u.ac.jp

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 23, 2008
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Summary

Non-equilibrium steady state analysis reveals two fluctuation-response relations. These formulas capture unique features of systems far from equilibrium, unlike those found in thermal equilibrium.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Thermodynamics

Background:

  • Linear response theory describes how systems react to small perturbations.
  • Equilibrium systems follow detailed balance, simplifying fluctuation-dissipation theorems.
  • Non-equilibrium systems lack detailed balance, leading to complex fluctuation behaviors.

Purpose of the Study:

  • To investigate fluctuation-response relations in non-equilibrium steady states (NESS) within the Gaussian regime.
  • To identify and characterize novel fluctuation-response relations specific to systems far from equilibrium.

Main Methods:

  • Linear response analysis applied to systems in a non-equilibrium steady state.
  • Analysis within the Gaussian regime, assuming near-equilibrium fluctuations.
  • Derivation of two independent fluctuation-response relations.

Main Results:

  • A symmetric fluctuation-response relation was derived, incorporating irreversible circulation to account for deviations from equilibrium.
  • An antisymmetric fluctuation-response relation was identified, linking asymmetries in fluctuations and response functions.
  • These relations were shown to be characteristic of non-equilibrium systems and absent in equilibrium.

Conclusions:

  • Two distinct fluctuation-response relations characterize linear response in NESS (Gaussian regime).
  • These relations highlight unique aspects of fluctuations far from equilibrium, offering new insights into non-equilibrium statistical mechanics.