Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Generalization of the fluctuation-dissipation theorem to classical nonequilibrium systems with anisotropic temperatures

J. Vogel, C. Toepffer

Published Jan 1, 1991• 1 citation
Publisher

Abstract

The fluctuation-dissipation theorem (FDT) in its kinetic form is generalized to anisotropic nonequilibrium states with more than one temperature. In a pseudoequilibrium, expressions for the generalized response functions and for the generalized correlation functions can be defined that preserve the form of a FDT in the classical limit.
DOI
10.1103/physreva.43.1090

Related papers

Fluctuation-dissipation theorem for non-equilibrium quantum systems

Mohammad Mehboudi, Anna Sanpera, Juan M. R. Parrondo

The fluctuation-dissipation theorem (FDT) is a central result in statistical physics, both for classical and quantum systems. It establishes a relationship between the linear response of a system under a time-dependent perturbation and time correlations of certain observables in equilibrium. Here we derive a generalization of the theorem which can be applied to any Markov quantum system and makes use of the symmetric logarithmic derivative (SLD). There are several important benefits from our approach. First, such a formulation clarifies the relation between classical and quantum versions of the equilibrium FDT. Second, and more important, it facilitates the extension of the FDT to arbitrary quantum Markovian evolution, as given by quantum maps. Third, it clarifies the connection between the FDT and quantum metrology in systems with a non-equilibrium steady state.

arXiv:1705.03968•Quantum•May 24, 2018•19 citations

Fluctuation-Dissipation Relation in a Nonequilibrium Quantum Fluid

T. R. Kirkpatrick, D. Belitz

There is no simple fluctuation-dissipation theorem (FDT) for nonequilibrium systems. We show that for a fluid in a nonequilibrium steady state (NESS) characterized by a constant temperature gradient there is a generalized FDT that relates commutator correlation functions to the bilinear response of products of observables. This allows for experimental probes of the long-range correlations in such a system, quantum or classical, via response experiments. We also show that the correlations are not tied to thermal fluctuations but are intrinsic to the NESS and reflect a generalized rigidity.

arXiv:2305.06406•Physical Review Letters•Dec 13, 2023•4 citations

Fluctuation-dissipation theorem for nonequilibrium quantum systems

Zhedong Zhang, Wei Wu, Jin Wang

We present a fluctuation-dissipation theorem (FDT) for nonequilibrium quantum systems with detailed-balance breaking, which deviates from the conventional form of the FDT for equilibrium systems preserving detailed balance. Using the phase space formulation of quantum mechanics and the potential-flux landscape framework, we find that the response function of nonequilibrium quantum systems to external perturbations contains a nontrivial contribution from the quantum curl flux quantifying detailed-balance breaking in the steady state, in addition to the correlation function of observables in the steady state representing the contribution of spontaneous fluctuations which is also present in the equilibrium FDT. We illustrate our general formalism with a harmonic oscillator coupled to two heat baths, and show that the nonequilibrium FDT reduces to the conventional expression at the equilibrium condition when the flux contribution vanishes.

Europhysics Letters (EPL)•Jul 1, 2016•7 citations

Generalized fluctuation-dissipation relation for quantum Markovian systems

Mohammad Mehboudi, Anna Sanpera, Juan M. R. Parrondo

The fluctuation-dissipation theorem (FDT) is a central result in statistical physics, both for classical and quantum systems. It establishes a relationship between the linear response of a system under a time-dependent perturbation and time correlations of certain observables in equilibrium. Here we derive a generalization of the theorem which can be applied to any Markov quantum system and makes use of the symmetric logarithmic derivative (SLD). There are several important benefits from our approach. First, such a formulation clarifies the relation between classical and quantum versions of the equilibrium FDT. Second, and more important, it facilitates the extension of the FDT to arbitrary quantum Markovian evolutions, as given by quantum maps. Third, it brings out the full connection between the FDT and the Quantum Fisher information, the figure of merit in quantum metrology.

•May 10, 2017•0 citations

Generalized fluctuation-dissipation theorem for nonlinear response functions

Enke Wang, Ulrich Heinz

A nonlinear generalization of the fluctuation-dissipation theorem (FDT) for the n-point Green functions and the amputated one particle irreducible vertex functions at finite temperature is derived in the framework of the closed time path formalism. We verify that this generalized FDT coincides with known results for $n=2$ and 3. New explicit relations among the 4-point nonlinear response and correlation (fluctuation) functions are presented.

arXiv:hep-th/9809016•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Jul 2, 2002•122 citations

Numerical Verification of the Fluctuation-Dissipation Theorem for Isolated Quantum Systems

Jae Dong Noh, Takahiro Sagawa, Joonhyun Yeo

The fluctuation-dissipation theorem (FDT) is a hallmark of thermal equilibrium systems in the Gibbs state. We address the question whether the FDT is obeyed by isolated quantum systems in an energy eigenstate. In the framework of the eigenstate thermalization hypothesis, we derive the formal expression for two-time correlation functions in the energy eigenstates or in the diagonal ensemble. They satisfy the Kubo-Martin-Schwinger condition, which is the sufficient and necessary condition for the FDT, in the infinite system size limit. We also obtain the finite size correction to the FDT for finite-sized systems. With extensive numerical works for the XXZ spin chain model, we confirm our theory for the FDT and the finite size correction. Our results can serve as a guide line for an experimental study of the FDT on a finite-sized system.

arXiv:2004.03917•Physical Review Letters•Jul 31, 2020•17 citations
The fluctuation-dissipation theorem (FDT) is a central result in statistical physics, both for classical and quantum systems. It establishes a relationship between the linear response of a system under a time-dependent perturbation and time correlations of certain observables in equilibrium. Here we derive a generalization of the theorem which can be applied to any Markov quantum system and makes use of the symmetric logarithmic derivative (SLD). There are several important benefits from our approach. First, such a formulation clarifies the relation between classical and quantum versions of the equilibrium FDT. Second, and more important, it facilitates the extension of the FDT to arbitrary quantum Markovian evolution, as given by quantum maps. Third, it clarifies the connection between the FDT and quantum metrology in systems with a non-equilibrium steady state.
There is no simple fluctuation-dissipation theorem (FDT) for nonequilibrium systems. We show that for a fluid in a nonequilibrium steady state (NESS) characterized by a constant temperature gradient there is a generalized FDT that relates commutator correlation functions to the bilinear response of products of observables. This allows for experimental probes of the long-range correlations in such a system, quantum or classical, via response experiments. We also show that the correlations are not tied to thermal fluctuations but are intrinsic to the NESS and reflect a generalized rigidity.
We present a fluctuation-dissipation theorem (FDT) for nonequilibrium quantum systems with detailed-balance breaking, which deviates from the conventional form of the FDT for equilibrium systems preserving detailed balance. Using the phase space formulation of quantum mechanics and the potential-flux landscape framework, we find that the response function of nonequilibrium quantum systems to external perturbations contains a nontrivial contribution from the quantum curl flux quantifying detailed-balance breaking in the steady state, in addition to the correlation function of observables in the steady state representing the contribution of spontaneous fluctuations which is also present in the equilibrium FDT. We illustrate our general formalism with a harmonic oscillator coupled to two heat baths, and show that the nonequilibrium FDT reduces to the conventional expression at the equilibrium condition when the flux contribution vanishes.
The fluctuation-dissipation theorem (FDT) is a central result in statistical physics, both for classical and quantum systems. It establishes a relationship between the linear response of a system under a time-dependent perturbation and time correlations of certain observables in equilibrium. Here we derive a generalization of the theorem which can be applied to any Markov quantum system and makes use of the symmetric logarithmic derivative (SLD). There are several important benefits from our approach. First, such a formulation clarifies the relation between classical and quantum versions of the equilibrium FDT. Second, and more important, it facilitates the extension of the FDT to arbitrary quantum Markovian evolutions, as given by quantum maps. Third, it brings out the full connection between the FDT and the Quantum Fisher information, the figure of merit in quantum metrology.
A nonlinear generalization of the fluctuation-dissipation theorem (FDT) for the n-point Green functions and the amputated one particle irreducible vertex functions at finite temperature is derived in the framework of the closed time path formalism. We verify that this generalized FDT coincides with known results for n=2n=2n=2 and 3. New explicit relations among the 4-point nonlinear response and correlation (fluctuation) functions are presented.
The fluctuation-dissipation theorem (FDT) is a hallmark of thermal equilibrium systems in the Gibbs state. We address the question whether the FDT is obeyed by isolated quantum systems in an energy eigenstate. In the framework of the eigenstate thermalization hypothesis, we derive the formal expression for two-time correlation functions in the energy eigenstates or in the diagonal ensemble. They satisfy the Kubo-Martin-Schwinger condition, which is the sufficient and necessary condition for the FDT, in the infinite system size limit. We also obtain the finite size correction to the FDT for finite-sized systems. With extensive numerical works for the XXZ spin chain model, we confirm our theory for the FDT and the finite size correction. Our results can serve as a guide line for an experimental study of the FDT on a finite-sized system.