Thermodynamic Equilibrium as a Symmetry of the Schwinger-Keldysh Action

Abstract

The time evolution of an extended quantum system can be theoretically described in terms of the Schwinger-Keldysh functional integral formalism, whose action conveniently encodes the information about the dynamics. We show here that the action of quantum systems evolving in thermal equilibrium is invariant under a symmetry transformation which distinguishes them from generic open systems. A unitary or dissipative dynamics having this symmetry naturally leads to the emergence of a Gibbs thermal stationary state. Moreover, the fluctuation-dissipation relations characterizing the linear response of an equilibrium system to external perturbations can be derived as the Ward-Takahashi identities associated with this symmetry. Accordingly, the latter provides an efficient check for the onset of thermodynamic equilibrium and it makes testing the validity of fluctuation-dissipation relations unnecessary. In the classical limit, this symmetry renders the one which is known to characterize equilibrium in the stochastic dynamics of classical systems coupled to thermal baths, described by Langevin equations.

24 pages, 1 figure; final published version

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Cited by in corpus (72)

• Keldysh Field Theory for Driven Open Quantum Systems
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• Driven Markovian Quantum Criticality
• Absorbing state phase transition with competing quantum and classical fluctuations
• Symmetry classes of open fermionic quantum matter
• Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos
• Effective Action for Relativistic Hydrodynamics: Fluctuations, Dissipation, and Entropy Inflow
• Universality in driven open quantum matter
• Schwinger-Keldysh formalism II: Thermal equivariant cohomology
• Quantum dynamical field theory for non-equilibrium phase transitions in driven open systems
• Non-equilibrium effective field theory for absorbing state phase transitions in driven open quantum spin systems
• Short-time universal scaling and light-cone dynamics after a quench in an isolated quantum system in $d$ spatial dimensions
• Thermal out-of-time-order correlators, KMS relations, and spectral functions
• Kibble-Zurek mechanism in driven-dissipative systems crossing a non-equilibrium phase transition
• Hidden time-reversal symmetry, quantum detailed balance and exact solutions of driven-dissipative quantum systems
• Tuning across Universalities with a Driven Open Condensate
• Lieb-Schultz-Mattis Theorem in Open Quantum Systems
• Phenomenology of a First Order Dark State Phase Transition
• Progress and Challenges in Small Systems
• From quantum to classical dynamics: The relativistic $O(N)$ model in the framework of the real-time functional renormalization group
• Far-from-equilibrium universality in the two-dimensional Heisenberg model
• Effective Lagrangian for Nambu-Goldstone modes in nonequilibrium open systems
• Spectral functions from the real-time functional renormalization group
• Many-Body Open Quantum Systems
• Universal short-time dynamics: boundary functional renormalization group for a temperature quench
• Effective field theory of time-translational symmetry breaking in nonequilibrium open system
• (Non) equilibrium dynamics: a (broken) symmetry of the Keldysh generating functional
• Emergent Supersymmetry in Local Equilibrium Systems
• Real-time methods for spectral functions
• Two roads to hydrodynamic effective actions: a comparison
• The Schwinger-Keldysh Coset Construction
• The Universal Time-Dependent Ginzburg-Landau theory
• Absence of Criticality in the Phase Transitions of Open Floquet Systems
• Kramers' degeneracy for open systems in thermal equilibrium
• Emergent Kardar-Parisi-Zhang phase in quadratically driven condensates
• Entropy and information flow in quantum systems strongly coupled to baths
• Revealing the nature of non-equilibrium phase transitions with quantum trajectories
• Topological gauge theory for mixed Dirac stationary states in all dimensions
• Pseudo-thermalization in driven-dissipative non-Markovian open quantum systems
• Axiomatic construction of quantum Langevin equations
• Lindblad dynamics of the quantum spherical model
• Dissipation dynamics of a scalar field
• Gauging anomalous unitary operators
• Atomic loss and gain as a resource for non-equilibrium phase transitions in optical lattices
• Hamiltonian formulation of systems with balanced loss-gain and exactly solvable models
• Dynamic renormalization group theory for open Floquet systems
• Vortex dynamics in a compact Kardar-Parisi-Zhang system
• Keldysh functional renormalization group for electronic properties of graphene
• Fluctuation Dissipation Relations for Active Field Theories
• Symmetry and its breaking in path integral approach to quantum Brownian motion
• Role of initial conditions in the dynamics of quantum glassy systems
• Propelling Ferrimagnetic Domain Walls by Dynamical Frustration
• Population Dynamics of Schrödinger Cats
• Double-trace deformation in Keldysh field theory
• Time-reversal symmetry breaking and emergence in driven-dissipative Ising models
• Far-from-equilibrium universality in two-dimensional Heisenberg antiferromagnets
• A convenient Keldysh contour for thermodynamically consistent perturbative and semiclassical expansions
• Replica symmetry breaking in spin glasses in the replica-free Keldysh formalism
• Extending quantum detailed balance through optimal transport
• Fluctuation Dissipation Relations for the Non-Reciprocal Cahn-Hilliard Model
• Effective Description of Ajar Systems with a $U(1)$ Symmetry
• Limitations of the Markovian approximation in the harmonic oscillator
• Classical Hamiltonian Systems with Balanced loss and gain
• Unifying quantum stochastic methods using Wick's theorem on the Keldysh contour
• Note on the super-extended Moyal formalism and its BBGKY hierarchy
• Space-time first-order correlations of an open Bose-Hubbard model with incoherent pump and loss
• Macroscopic Quantum States and Universal Correlations in a Disorder-Order Interface Propagating over a 1D Ground State
• Quantum detailed balance via elementary transitions
• Emergent structures in open EFTs
• Schwinger-Keldysh path integral formalism for a Quenched Quantum Inverted Oscillator