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Outofequilibrium dynamics of two interacting opticallytrapped particles
by Victor S Dotsenko, Alberto Imparato, Pascal Viot, Gleb Oshanin
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Submission summary
Authors (as registered SciPost users):  Pascal Viot 
Submission information  

Preprint Link:  https://arxiv.org/abs/2302.07716v1 (pdf) 
Date accepted:  20230530 
Date submitted:  20230216 08:46 
Submitted by:  Viot, Pascal 
Submitted to:  SciPost Physics Core 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We present a theoretical analysis of a nonequilibrium dynamics in a model system consisting of two particles which move randomly on a plane. The two particles interact via a harmonic potential, experience their own (independent from each other) noises characterized by two different temperatures $T_1$ and $T_2$, and each particle is being held by its own optical tweezer. Such a system with two particle coupled by hydrodynamic interactions was previously realised experimentally in B\'erut et al. [EPL {\bf 107}, 60004 (2014)], and the difference between two temperatures has been achieved by exerting an additional noise on either of the tweezers. Framing the dynamics in terms of two coupled overdamped Langevin equations, we show that the system reaches a nonequilibrium steadystate with nonzero (for $T_1 \neq T_2$) probability currents that possess nonzero curls. As a consequence, in this system the particles are continuously spinning around their centers of mass in a completely synchronised way  the curls of currents at the instantaneous positions of two particles have the same magnitude and sign. Moreover, we demonstrate that the components of currents of two particles are strongly correlated and undergo a rotational motion along closed elliptic orbits.
Published as SciPost Phys. Core 6, 056 (2023)
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 202359 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2302.07716v1, delivered 20230509, doi: 10.21468/SciPost.Report.7173
Strengths
 Clearly defined problem and solid solution
 Of experimental relevance
 Wellwritten and pedagogical
 Appears to be sound and correct
Weaknesses
 Extends earlier work, rather than being completely original and novel.
Report
The authors investigate theoretically the nonequilibrium dynamics of two interacting particles that move randomly in a plane under the influence of different temperatures. Such a setup has recently been realized experimentally using optical tweezers with effective temperatures implemented by additional noise. The authors find that the particles spin around their centersofmass in a synchronised way. Compared to earlier works that focused on a onedimensional setup, the authors now consider a plane and unravel the dynamical behavior that can occur in two dimensions.
I like the paper and believe that it can be published as it is. The problem is clearly laid out, and the solution seems correct and sound. The findings may also be of relevance to current experimental actitivies.
I just have a few minor comments for the authors to consider:
 I wonder if one can interpret the normalization factor in Eqs. (10,24), with the suggestive letter Z, as a nonequilibrium partition function? If so, would it be possible to extract further information from this quantity, for example, by going beyond average values and consider fluctuations as well?
 The authors might want to proofread the manuscript one last time; e.g. in the caption of Fig. 4, there is a typo in "averaged".