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(Non) equilibrium dynamics: a (broken) symmetry of the Keldysh generating functional
by Camille Aron, Giulio Biroli, Leticia F. Cugliandolo
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Submission summary
Authors (as registered SciPost users):  Camille Aron 
Submission information  

Preprint Link:  http://arxiv.org/abs/1705.10800v3 (pdf) 
Date accepted:  20180121 
Date submitted:  20171221 01:00 
Submitted by:  Aron, Camille 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We unveil the universal (modelindependent) symmetry satisfied by SchwingerKeldysh quantum field theories whenever they describe equilibrium dynamics. This is made possible by a generalization of the SchwingerKeldysh pathintegral formalism in which the physical time can be reparametrized to arbitrary contours in the complex plane. Strong relations between correlation functions, such as the fluctuationdissipation theorems, are derived as immediate consequences of this symmetry of equilibrium. In this view, quantum nonequilibrium dynamics  e.g. when driving with a timedependent potential  are seen as symmetrybreaking processes. The symmetrybreaking terms of the action are identified as a measure of irreversibility, or entropy creation, defined at the level of a single quantum trajectory. Moreover, they are shown to obey quantum fluctuation theorems. These results extend stochastic thermodynamics to the quantum realm.
Published as SciPost Phys. 4, 008 (2018)
Author comments upon resubmission
While both Referees acknowledged the significance and the originality of our work, they also pointed out that, given the rather formal nature of our approach, additional efforts could be made to better present the physical findings. We fully agree with the Referees, and we thank them for their suggestions in that respect, which we followed (see the List of changes).
We hope that the referees will find the revised version of our manuscript suitable for publication in SciPost without further delay.
Camille Aron
Giulio Biroli
Leticia F. Cugliandolo
List of changes
 We revised the introductory Section 1.1 "Motivations" to better appeal to the community of quantum thermodynamics by articulating one of our main findings, namely the identification of a quantum version of the irreversible entropy production rate, in the context of what has already been achieved in the classical realm (stochastic thermodynamics), and of the questions that are still debated in the quantum realm.
 We revised the introductory Section 1.3 "Main results", paragraph "Outofequilibrium dynamics", by announcing a later discussion on a concrete and simple model where our findings can be worked out and discussed explicitly, numerically or even experimentally.
 We added the corresponding discussion in Sect. 4.2 "Symmetry breaking term", where we consider a twolevel system (TLS) which is driven through an avoided crossing at different rates. Despite its simplicity, the timedependent driven TLS has two virtues:
(i) it belongs to a different `class' of systems than the bosonic and fermionic fields that are treated in the rest of the manuscript. The TLS is an SU(2) symmetric object with a more cumbersome pathintegral representation, however the quantum thermodynamic operators that were derived using bosonic and fermionic fields are readily applicable to any quantum mechanical system,
(ii) the excitations created when ramping across the avoided crossing at a finite rate are of purely quantum mechanical origin (contrary to the case of, say, a driven quantum harmonic oscillator which comes with a 'classical' intuition/phenomenology). While the evolution is purely unitary, it is clear that these tunnel excitations can be associated to the production of irreversibility in the system.
The novel quantity $\langle \Sigma \rangle$ is studied numerically in different regimes, and compared to the work $\langle \mathcal{W} \rangle$. This simple model is used again in Section 4.3 "Quantum fluctuation theorems", paragraph "Jarzynski equality", to illustrate our proposed definition of irreversibility production, $\mathcal{S}_{irr}$, given in Eqs. (100) and (104).
Submission & Refereeing History
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Reports on this Submission
Anonymous Report 1 on 20171221 (Invited Report)
 Cite as: Anonymous, Report on arXiv:1705.10800v3, delivered 20171221, doi: 10.21468/SciPost.Report.305
Report
The authors have seriously taken into consideration my advice contained in the previous report. I am glad to assess that now the paper is an interesting and complete piece of science, with both technical and practical aspects of interest for the community working in nonequilibrium many body physics.