Thermal noise of mechanical oscillators in steady states with a heat flux

Livia Conti, Claudia Lazzaro, Gagik Karapetyan, Michele Bonaldi, Matteo Pegoraro, Ram-Krishna Thakur, Paolo De Gregorio, and Lamberto Rondoni
Phys. Rev. E 90, 032119 – Published 17 September 2014

Abstract

We present an experimental investigation of the statistical properties of the position fluctuations of low-loss oscillators in nonequilibrium steady states. The oscillators are coupled to a heat bath, and a nonequilibrium steady state is produced by flowing a constant heat flux, setting a temperature difference across the oscillators. We investigated the distribution of the measurements of the square of the oscillator position and searched for signs of changes with respect to the equilibrium case. We found that, after normalization by the mean value, the second, third, and fourth standardized statistical moments are not modified by the underlying thermodynamic state. This differs from the behavior of the absolute, i.e., not normalized, second moment, which is strongly affected by temperature gradients and heat fluxes. We illustrate this with a numerical experiment in which we study via molecular dynamics the fluctuations of the length of a one-dimensional chain of identical particles interacting via anharmonic interparticle potentials, with the extremes thermostated at different temperatures: we use the variance of the length in correspondence to its first elastic mode of resonance to define an effective temperature which we observe to depart from the thermodynamic one in the nonequilibrium states. We investigate the effect of changing the interparticle potential and show that the qualitative behavior of the nonequilibrium excess is unchanged. Our numerical results are consistent with the chain length being Gaussian distributed in the nonequilibrium states. Our experimental investigation reveals that the position variance is the only, and crucially easily accessible, observable for distinguishing equilibrium from nonequilibrium steady states. The consequences of this fact for the design of interferometric gravitational wave detectors are discussed.

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  • Received 19 February 2014
  • Revised 24 June 2014

DOI:https://doi.org/10.1103/PhysRevE.90.032119

©2014 American Physical Society

Authors & Affiliations

Livia Conti1,*, Claudia Lazzaro1, Gagik Karapetyan1, Michele Bonaldi2,3, Matteo Pegoraro1, Ram-Krishna Thakur1, Paolo De Gregorio1, and Lamberto Rondoni4,5

  • 1Istituto Nazionale di Fisica Nucleare, Via Marzolo 8, I-35131 Padova, Italy
  • 2Institute of Materials for Electronics and Magnetism, Nanoscience-Trento-FBK Division, 38123 Povo (Trento), Italy
  • 3Istituto Nazionale di Fisica Nucleare, Trento Institute for Fundamental Physics and Applications, 38123 Povo (Trento), Italy
  • 4Dipartimento di Scienze Matematiche and Graphene@PoliTO Lab, Politecnico di Torino Corso Duca degli Abruzzi 24, 10129 Torino, Italy
  • 5Istituto Nazionale di Fisica Nucleare, Sezione di Torino, Via P. Giura 1, 10125 Torino, Italy

  • *Corresponding author: lconti@pd.infn.it

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Issue

Vol. 90, Iss. 3 — September 2014

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