Inertialess gyrating engines

Abstract

A typical model for a gyrating engine consists of an inertial wheel powered by an energy source that generates an angle-dependent torque. Examples of such engines include a pendulum with an externally applied torque, Stirling engines, and the Brownian gyrating engine. Variations in the torque are averaged out by the inertia of the system to produce limit cycle oscillations. While torque generating mechanisms are also ubiquitous in the biological world, where they typically feed on chemical gradients, inertia is not a property that one naturally associates with such processes. In the present work, seeking ways to dispense of the need for inertial effects, we study an inertia-less concept where the combined effect of coupled torque-producing components averages out variations in the ambient potential and helps overcome dissipative forces to allow sustained operation for vanishingly small inertia. We exemplify this inertia-less concept through analysis of two of the aforementioned engines, the Stirling engine and the Brownian gyrating engine. An analogous principle may be sought in biomolecular processes as well as in modern-day technological engines, where for the latter, the coupled torque-producing components reduce vibrations that stem from the variability of the generated torque.

Cooperative dynamics in two-component out-of-equilibrium systems: molecular ‘spinning tops’

“…(35) and (36) contain the first inverse power of time, as can be expected from the "diffusive" growth of the second moments of positions and the velocities (see Eqs. ( 18) and (19), and also Eqs. ( 23) and ( 24)), while the amplitudes of the cross-terms decay at a faster rate proportional to 1/t 2 , showing that the velocities effectively decouple from the positions in the large-t limit.…”

“…Note also that the frequencies Ω pm are continuous functions of λ and u, hence, are incommensurate generically, resulting in the irregular oscillations of all terms except the first ones in Eqs. ( 18) and (19).…”

“…of Eqs. ( 18) and (19). These terms, proportional to T 1 − T 2 , are denoted here and below by square brackets.…”

“…We observe that the covariance depends only on the sum of the temperatures, unlike the moments x 2 and y 2 in Eqs. (18) and (19). The leading large-t term of Eq.…”

“…Various aspects of the dynamical and the steady-state behavior of the BGM have been analyzed in case of standard delta-correlated in time noises acting on the position components of the particle (see, e.g., [11][12][13][14][15][16][17][18][19][20]) and also for the noises with long-ranged temporal correlations [21,22]. Few examples of problems that have been studied are the entropy production [23,24], effects of anisotropic fluctuations [25,26] and nonharmonic potentials [27], rotational dynamics of a Brownian ellipsoid in isotropic potential or of an inertial chiral ellipsoid [28], the spectral properties of individual trajectories of a gyrator [29,30], emerging cooperative behavior of several Brownian gyrators [31,32], as well as the synchronization of two out-of-equilibrium Kuramoto oscillators living at different temperatures [33].…”