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

Progress of Theoretical Physics

On Statistical Mechanics of Nonequilibrium Fluctuations

M. Ichiyanagi

Published Jun 1, 1984• 0 citations
Publisher

Abstract

Without assuming detailed balance, the linear response theory of systems, in which the notation of a quantum dynamical semigroup can be defined, is discussed. This theory is used to prove a fluctuation-dissipation theorem for nonstationary nonequilibrium states. We propose an extended version of the Liouville equation in which we incorporate the stochastic behavior of the subsystem of the macroscopic motions. For this we introduce a non-Hermitian Hamiltonian and set a Liouville equation for a density matrix which is not Hermitian. We show that a response to external perturbations reduces to a sum of two contributions, one for which an improved fluctuation-dissipation theorem is proved and the other due to stochastic excitations that does not satisfy a reciprocity relation of Onsager type.

DOI
10.1143/ptp.71.1152

Related papers

Fluctuation Relations for Quantum Markovian Dynamical System

Raphaël Chétrite, Kirone Mallick

We derive a general set of fluctuation relations for a nonequilibrium open quantum system described by a Lindblad master equation. In the special case of conservative Hamiltonian dynamics, these identities allow us to retrieve quantum versions of Jarzynski and Crooks relations. In the linear response regime, these fluctuation relations yield a fluctuation-dissipation theorem (FDT) valid for a stationary state arbitrarily far from equilibrium. For a closed system, this FDT reduces to the celebrated Callen-Welton-Kubo formula.

arXiv:1002.0950•Feb 4, 2010•1 citation

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

Linear response theory for quantum Gaussian processes

Mohammad Mehboudi, Juan M R Parrondo, Antonio Acín

Abstract Fluctuation dissipation theorems (FDTs) connect the linear response of a physical system to a perturbation to the steady-state correlation functions. Until now, most of these theorems have been derived for finite-dimensional systems. However, many relevant physical processes are described by systems of infinite dimension in the Gaussian regime. In this work, we find a linear response theory for quantum Gaussian systems subject to time dependent Gaussian channels. In particular, we establish a FDT for the covariance matrix that connects its linear response at any time to the steady state two-time correlations. The theorem covers non-equilibrium scenarios as it does not require the steady state to be at thermal equilibrium. We further show how our results simplify the study of Gaussian systems subject to a time dependent Lindbladian master equation. Finally, we illustrate the usage of our new scheme through some examples. Due to broad generality of the Gaussian formalism, we expect our results to find an application in many physical platforms, such as opto-mechanical systems in the presence of external noise or driven quantum heat devices.

arXiv:1901.05709•New Journal of Physics•Jul 11, 2019•11 citations

Linear response theory for quantum Gaussian processes

Mohammad Mehboudi, Rodríguez Parrondo, Juan Manuel, Antonio Acín

Fluctuation dissipation theorems (FDTs) connect the linear response of a physical system to a perturbation to the steady-state correlation functions. Until now, most of these theorems have been derived for finite-dimensional systems. However, many relevant physical processes are described by systems of infinite dimension in the Gaussian regime. In this work, we find a linear response theory for quantum Gaussian systems subject to time dependent Gaussian channels. In particular, we establish a FDT for the covariance matrix that connects its linear response at any time to the steady state two-time correlations. The theorem covers non-equilibrium scenarios as it does not require the steady state to be at thermal equilibrium. We further show how our results simplify the study of Gaussian systems subject to a time dependent Lindbladian master equation. Finally, we illustrate the usage of our new scheme through some examples. Due to broad generality of the Gaussian formalism, we expect our results to find an application in many physical platforms, such as opto-mechanical systems in the presence of external noise or driven quantum heat devices.

•Aug 21, 2019•9 citations

Universal Fluctuation-Dissipation Theorem for Non-Hermitian Quantum Systems

Revista, Zen, PHYSICS, 10

The fluctuation-dissipation theorem (FDT) is a cornerstone of statistical mechanics, linking the linear response of a system to external perturbations with the equilibrium fluctuations of its constituent degrees of freedom. Traditionally formulated for Hermitian quantum systems in thermal equilibrium, its applicability to non-Hermitian quantum systems, which are increasingly relevant in areas such as open quantum systems, PT-symmetric quantum mechanics, and topological phases, remains a complex and largely unresolved challenge. This paper presents a theoretical framework for a universal fluctuation-dissipation theorem applicable to a broad class of non-Hermitian quantum systems. We demonstrate how the presence of non-Hermiticity, characterized by complex energy eigenvalues and non-orthogonal eigenstates, fundamentally modifies the relationship between correlation functions and response functions. Our derivation utilizes a generalized time-evolution operator and incorporates concepts from non-Hermitian spectral theory, revealing a modified FDT that accounts for energy gain or loss inherent in these systems. The resulting theorem provides insights into the interplay between quantum noise and dissipation in environments far from conventional thermal equilibrium, offering a crucial tool for understanding and engineering non-Hermitian quantum devices. We discuss the implications for non-equilibrium steady states and the breakdown of standard notions of temperature and entropy, proposing a path towards experimental verification in platforms like photonic lattices and cold atoms with controlled losses.

•Nov 28, 2025•0 citations

A Contribution to the Theory of Nonequilibrium Statistical Mechanics. II. Nonequilibrium Density Matrix

Masakazu Ichiyanagi

The concept proposed by Kirkwood that a macroscopic quantity is the time average of the ensemble average of the corresponding dynamical operator is examined in detail. This concept provides us with a new possibility of studying nonequilibrium macroscopic systems. The method to be used here is based on the fact that a time-smoothed density matrix also satisfies the original Liouville-von Neumann equation for the unsmoothed one. Forms of nonequilibritum density matrix are given as exact solutions to it. In characterizing thermodynamically the density operators the use of the Gibbs-Duhem relation is made. A generalized version of Kubo formula is obtained for nonequilibrium systems in the hydrodynamical stage. The present method is also applicable to nonlinear dynamical systems.

Journal of the Physical Society of Japan•Jul 15, 1989•3 citations
Without assuming detailed balance, the linear response theory of systems, in which the notation of a quantum dynamical semigroup can be defined, is discussed. This theory is used to prove a fluctuation-dissipation theorem for nonstationary nonequilibrium states. We propose an extended version of the Liouville equation in which we incorporate the stochastic behavior of the subsystem of the macroscopic motions. For this we introduce a non-Hermitian Hamiltonian and set a Liouville equation for a density matrix which is not Hermitian. We show that a response to external perturbations reduces to a sum of two contributions, one for which an improved fluctuation-dissipation theorem is proved and the other due to stochastic excitations that does not satisfy a reciprocity relation of Onsager type.
We derive a general set of fluctuation relations for a nonequilibrium open quantum system described by a Lindblad master equation. In the special case of conservative Hamiltonian dynamics, these identities allow us to retrieve quantum versions of Jarzynski and Crooks relations. In the linear response regime, these fluctuation relations yield a fluctuation-dissipation theorem (FDT) valid for a stationary state arbitrarily far from equilibrium. For a closed system, this FDT reduces to the celebrated Callen-Welton-Kubo formula.
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.
Abstract Fluctuation dissipation theorems (FDTs) connect the linear response of a physical system to a perturbation to the steady-state correlation functions. Until now, most of these theorems have been derived for finite-dimensional systems. However, many relevant physical processes are described by systems of infinite dimension in the Gaussian regime. In this work, we find a linear response theory for quantum Gaussian systems subject to time dependent Gaussian channels. In particular, we establish a FDT for the covariance matrix that connects its linear response at any time to the steady state two-time correlations. The theorem covers non-equilibrium scenarios as it does not require the steady state to be at thermal equilibrium. We further show how our results simplify the study of Gaussian systems subject to a time dependent Lindbladian master equation. Finally, we illustrate the usage of our new scheme through some examples. Due to broad generality of the Gaussian formalism, we expect our results to find an application in many physical platforms, such as opto-mechanical systems in the presence of external noise or driven quantum heat devices.
Fluctuation dissipation theorems (FDTs) connect the linear response of a physical system to a perturbation to the steady-state correlation functions. Until now, most of these theorems have been derived for finite-dimensional systems. However, many relevant physical processes are described by systems of infinite dimension in the Gaussian regime. In this work, we find a linear response theory for quantum Gaussian systems subject to time dependent Gaussian channels. In particular, we establish a FDT for the covariance matrix that connects its linear response at any time to the steady state two-time correlations. The theorem covers non-equilibrium scenarios as it does not require the steady state to be at thermal equilibrium. We further show how our results simplify the study of Gaussian systems subject to a time dependent Lindbladian master equation. Finally, we illustrate the usage of our new scheme through some examples. Due to broad generality of the Gaussian formalism, we expect our results to find an application in many physical platforms, such as opto-mechanical systems in the presence of external noise or driven quantum heat devices.
The fluctuation-dissipation theorem (FDT) is a cornerstone of statistical mechanics, linking the linear response of a system to external perturbations with the equilibrium fluctuations of its constituent degrees of freedom. Traditionally formulated for Hermitian quantum systems in thermal equilibrium, its applicability to non-Hermitian quantum systems, which are increasingly relevant in areas such as open quantum systems, PT-symmetric quantum mechanics, and topological phases, remains a complex and largely unresolved challenge. This paper presents a theoretical framework for a universal fluctuation-dissipation theorem applicable to a broad class of non-Hermitian quantum systems. We demonstrate how the presence of non-Hermiticity, characterized by complex energy eigenvalues and non-orthogonal eigenstates, fundamentally modifies the relationship between correlation functions and response functions. Our derivation utilizes a generalized time-evolution operator and incorporates concepts from non-Hermitian spectral theory, revealing a modified FDT that accounts for energy gain or loss inherent in these systems. The resulting theorem provides insights into the interplay between quantum noise and dissipation in environments far from conventional thermal equilibrium, offering a crucial tool for understanding and engineering non-Hermitian quantum devices. We discuss the implications for non-equilibrium steady states and the breakdown of standard notions of temperature and entropy, proposing a path towards experimental verification in platforms like photonic lattices and cold atoms with controlled losses.
The concept proposed by Kirkwood that a macroscopic quantity is the time average of the ensemble average of the corresponding dynamical operator is examined in detail. This concept provides us with a new possibility of studying nonequilibrium macroscopic systems. The method to be used here is based on the fact that a time-smoothed density matrix also satisfies the original Liouville-von Neumann equation for the unsmoothed one. Forms of nonequilibritum density matrix are given as exact solutions to it. In characterizing thermodynamically the density operators the use of the Gibbs-Duhem relation is made. A generalized version of Kubo formula is obtained for nonequilibrium systems in the hydrodynamical stage. The present method is also applicable to nonlinear dynamical systems.