Correlations and responses for a system of n coupled linear oscillators with asymmetric interactions

Abstract

We focus on the asymmetry of the interaction in the optimal velocity (OV) model, which is a model of self-driven particles, and analytically investigate the effects of the asymmetry on the fluctuation-response relation, which is one of the remarkable relationships in statistical physics. By linearizing a modified OV model, i.e., the backward-looking optimal velocity model, which can easily control the magnitude of asymmetry in the interaction, we derive n coupled linear oscillators with asymmetric interactions. We analytically solve the equations of the n coupled linear oscillators and calculate the response and correlation functions. We find that the fluctuation response relation does not hold in the n coupled linear oscillators with asymmetric interactions. Moreover, as the magnitude of the asymmetry increases, the difference between the response and correlation functions increases .

Long range correlations and slow time scales in a boundary driven granular model

“…( 5 ) combined with physical constraint on . The former strategy, used by us and recently applied in 22 , 25 , when possible, is more convenient because it gives access also to time-dependent properties. The latter has been used to study temperature profiles in non-equilibrium harmonic chains 20 .…”

“…Lattices (particularly in 1d) bring two main advantages: (1) analytical calculations are often possible, (2) they help to isolate minimal ingredients for the occurrence of the phenomenon under study. Considering just the non-equilibrium context, 1D models have been used to study thermal conduction 20 – 22 , non-equilibrium fluctuations 23 , 24 , correlations and response with non-symmetric couplings 25 , velocity alignment in active matter 26 , systems with Vicsek-like interactions 27 , 28 , velocity fields in granular materials 29 – 31 . In the following we will just consider linear interactions between variables and this allows to work in the framework of multivariate linear stochastic processes.…”

Response and flux of information in extended non-equilibrium dynamics

“…This can be seen as the overdamped limit of a system of coupled linear oscillators with asymmetric interactions (see Ref. [20] for a detailed analytical discussion of the underdamped case). After that, the effect of nonlinearities will be taken into account.…”

“…For this class of linear models, we can exploit exact relations for the computation of Σ and RFs, as discussed in the previous section, and also of TEs, as detailed in Appendix A. Similar studies on systems with asymmetric linear interactions have been performed, for instance, in Ref [20]. First we focus on the case in which all noises have equal amplitudes, i.e.…”

Non-homogeneous Heating induces Scale-free Correlations and Slow time Scales in a Granular-like Velocity Field

“…Lattices (particularly in 1d) bring two main advantages: (i) analytical calculations are often possible, (ii) they help to isolate minimal ingredients for the occurrence of the phenomenon under study. Considering just the non-equilibrium context, 1D models have been used to study thermal conduction [19][20][21] , non-equilibrium fluctuations 22,23 , correlations and response with arXiv:2101.09516v1 [cond-mat.stat-mech] 23 Jan 2021 non-symmetric couplings 24 , velocity alignment in active matter 25 , systems with Vicsek-like interactions 26,27 , velocity fields in granular materials [28][29][30] . In the following we'll just consider linear interactions between variables and this allows to work in the framework of multivariate linear stochastic processes.…”