Asymmetry relations and effective temperatures for biased Brownian gyrators
Abstract
We focus on a paradigmatic twodimensional model of a nanoscale heat engine, the socalled Brownian gyrator, whose stochastic dynamics is described by a pair of coupled Langevin equations with different temperature noise terms. This model is known to produce a curlcarrying nonequilibrium steadystate with persistent angular rotations. We generalize the original model introducing constant forces doing work on the gyrator, for which we derive exact asymmetry relations, that are reminiscent of the standard fluctuation relations. Unlike the latter, our relations concern instantaneous and not time averaged values of the observables of interest. We investigate the full twodimensional dynamics as well as the dynamics projected on the x and y axes, so that information about the state of the system can be obtained from just a part of its degrees of freedom. Such a state is characterized by effective "temperatures" that can be measured in nanoscale devices, but do not have a thermodynamic nature. Remarkably, the effective temperatures appearing in full dynamics are distinctly different from the ones emerging in its projections, confirming that they are not thermodynamic quantities, although they precisely characterize the state of the system.
 Publication:

Physical Review E
 Pub Date:
 October 2018
 DOI:
 10.1103/PhysRevE.98.042149
 arXiv:
 arXiv:1810.02580
 Bibcode:
 2018PhRvE..98d2149C
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 6 pages, 1 figure