Thermodynamic equilibrium as a symmetry of the Schwinger-Keldysh action

Abstract

Extended quantum systems can be theoretically described in terms of the Schwinger-Keldysh functional integral formalism, whose action conveniently describes both dynamical and static properties. We show here that in thermal equilibrium, defined by the validity of fluctuation-dissipation relations, the action of a quantum system is invariant under a certain symmetry transformation and thus it is distinguished from generic systems. In turn, the fluctuation-dissipation relations can be derived as the Ward-Takahashi identities associated with this symmetry. Accordingly, the latter provides an efficient test for the onset of thermodynamic equilibrium and it makes checking the validity of fluctuation-dissipation relations unnecessary. In the classical limit, this symmetry reduces to the well-known one which characterizes equilibrium in the stochastic dynamics of classical systems coupled to thermal baths, described by Langevin equations. PACS numbers: 05.30.Jp,05.40.-a,05.70.Ln arXiv:1505.00912v2 [cond-mat.stat-mech] 10 Nov 2015

Emergent supersymmetry in local equilibrium systems

“…3 Additional condition(s) then need to be imposed on I eff for (1.4) to satisfy (1.11). For variables χ r,a associated with non-conserved quantities, the required symmetry is well known, probably since 70's [21,28,29]. In this case the couplings between χ r,a and external sources are the standard ones…”

Keldysh field theory for driven open quantum systems

“…The tilde on the RHS of the equation indicates that all external fields appearing, S have to be replaced by their corresponding time-reversed values. To name an example, the signs of magnetic fields have to be inverted [189]. Evidently, discussing a single symmetry instead of an infinite hierarchy of equations is much more elegant and practical: checking whether a given Keldysh action obeys Eq.…”

“…(16) is not compatible with equilibrium conditions: see Refs. [187][188][189], and the discussion in Sec. II D 1.)…”

Absorbing State Phase Transition with Competing Quantum and Classical Fluctuations

“…Several among these instances employ excitation of the atoms to high-lying Rydberg orbitals [24][25][26] in order to achieve strong interatomic interactions and to study cooperative effects [27][28][29]. In all these systems, the driving/dissipation introduces coherence loss and explicitly violates the equilibrium conditions at the microscopic level [7,30]. It is thus a challenge to identify to what extent the non-equilibrium and the quantum nature of the dynamics impact on the macroscopic phase diagram and phase transition properties.…”

“…This occurs when such out-of-equilibrium systems start to act collectively [1][2][3][4]. On a fundamental level, a distinction arises depending on the presence or absence of detailed balance [5][6][7][8], between systems which evolve towards a stationary equilibrium state (e.g., quenched systems coupled to thermal baths [9]) or that preserve their nonequilibrium character even in the long-time limit, representing flux equilibrium states. The universal dynamical features of purely classical systems have been extensively studied and classified both for unbroken [10] and broken [11][12][13][14] detailed balance, i.e., genuine non-equilibrium systems.…”