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When a DC source is suddenly disconnected from an RL (Resistor-Inductor) circuit, the circuit becomes source-free. Assuming the inductor has an initial current denoted as I0, the initial energy stored in the inductor can be determined.
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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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Nonequilibrium fluctuation-response relations for state-current correlations.

Krzysztof Ptaszyński1, Timur Aslyamov2, Massimiliano Esposito2

  • 1Institute of Molecular Physics, Polish Academy of Sciences, Mariana Smoluchowskiego 17, 60-179 Poznań, Poland.

Physical Review. E
|March 20, 2026
PubMed
Summary
This summary is machine-generated.

New fluctuation-response relations (FRRs) extend to mixed state-current observables in nonequilibrium systems. These findings clarify Onsager symmetry breaking and have applications in quantum dots and enzymatic networks.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Thermodynamics
  • Physical Chemistry

Background:

  • Exact fluctuation-response relations (FRRs) have been established for nonequilibrium steady states of Markov jump processes.
  • These FRRs connect fluctuations of observables to their responses to perturbations in transition rates.

Purpose of the Study:

  • To derive FRRs for mixed covariances involving one state and one current observable.
  • To develop inverse FRRs that express individual responses using covariances.
  • To investigate the conditions for Onsager symmetry breaking.

Main Methods:

  • Derivation of generalized fluctuation-response relations for Markov jump processes.
  • Analysis of mixed state-current covariances.
  • Application of derived relations to understand Onsager symmetry.

Main Results:

  • Analogous FRRs derived for mixed covariances of state and current observables.
  • Inverse FRRs developed, expressing responses in terms of covariances.
  • Demonstrated that state-current correlations are necessary for breaking Onsager symmetry.

Conclusions:

  • The study extends FRRs to mixed state-current observables, providing deeper insights into non-equilibrium systems.
  • The findings offer practical applications in understanding fluctuations in quantum dot devices and enzymatic reaction networks.