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This study investigates the suitability of the annealed approximation in high-dimensional systems characterized by dense networks with quenched link disorder, employing models of coupled oscillators. We demonstrate that dynamic equations governing dense-network systems converge to those of the complete-graph version in the thermodynamic limit, where link disorder fluctuations vanish entirely. Consequently, the annealed-network systems, where fluctuations are attenuated, also exhibit the same dynamic behavior in the thermodynamic limit. However, a significant discrepancy arises in the incoherent (disordered) phase wherein the finite-size behavior becomes critical in determining the steady-state pattern. To explicitly elucidate this discrepancy, we focus on identical oscillators subject to competitive attractive and repulsive couplings. In the incoherent phase of dense networks, we observe the manifestation of random irregular states. In contrast, the annealed approximation yields a symmetric (regular) incoherent state where two oppositely coherent clusters of oscillators coexist, accompanied by the vanishing order parameter. Our findings imply that the annealed approximation should be employed with caution even in dense-network systems, particularly in the disordered phase. [ABSTRACT FROM AUTHOR]

We present an experimental realization of an information-driven Brownian motor by periodically cooling a Brownian particle trapped in a harmonic potential connected to a single heat bath, where cooling is carried out by the information process consisting of measurement and feedback control. We show that the random motion of the particle is rectified by symmetry-broken feedback cooling where the particle is cooled only when it resides on the specific side of the potential center at the instant of measurement. Studying how the motor thermodynamics depends on cycle period τ relative to the relaxation time τB of the Brownian particle, we find that the ratcheting of thermal noise produces the maximum work extraction when τ ≥ 5τB, while the extracted power is maximum near τ = τB, implying the optimal operating time for the ratcheting process. In addition, we find that the average transport velocity is monotonically decreased as τ increases and present the upper bound for the velocity. [ABSTRACT FROM AUTHOR]