Stochastic thermodynamics in many-particle systems

Abstract

We study the thermodynamic properties of a microscopic model of coupled oscillators that exhibits a dynamical phase transition from a desynchronized to a synchronized phase. We consider two different configurations for the thermodynamic forces applied on the oscillators, one resembling the macroscopic power grids, and one resembling autonomous molecular motors. We characterize the input and the output power as well as the efficiency at maximum power, providing analytic expressions for such quantities near the critical coupling strength. We discuss the role of the quenched disorder in the thermodynamic force distributions and show that such a disorder may lead to an enhancement of the efficiency at maximum power.OPEN ACCESS RECEIVED exclusion process on a single lattice [8,25], or on a network [26]. In these studies, we found an increase of the EMP in a many-motor system with respect to the single motor case, for a suitable choice of the model parameters. Remarkably,in [8,25] we found that the enhancement of the EMP occurs in a range of parameter values compatible with the biological estimates for the molecular motor Kinesin. From those studies we concluded that after a dynamical phase transition the dynamical response of the system to an external drive can change, leading in turn to a change in the thermodynamic properties. Specifically the dependence of the delivered power on the driving thermodynamic forces may vary.One of the main limitation that one faces when studying the thermodynamic properties of exclusion processes on a lattice, is that the intensity of interaction between the motors can only be indirectly tuned by changing the kinetic parameters and thus the density of motors on the lattice [8,25,26]. Furthermore, if one wants to study the effect of force disorder on the motor particles, one has to resort to numerical simulations, as no exact result exists for the exclusion process with heterogeneous particles.Instead, here we consider a model of N interacting microscopic particles, where the particle-particle interaction is an explicit parameter, that can be tuned in order to drive a dynamical phase transition, from a weakly interacting-incoherent system to a strongly interacting-coherent system. This model was originally introduced by Sakaguchi in [27] as an extension of the Kuramoto model (KM) [28], to study the synchronization of a group of interacting oscillators in contact with a reservoir at constant temperature [29,30]. Furthermore, the effect of quenched disorder in the thermodynamic force distribution can be taken into account within the present model. The model is introduced and discussed in section 2. The N interacting particles can be viewed as a network of energy producers and users or as a system of interacting autonomous motors under the effect of thermodynamic forces. Since the dynamical phase diagram can be obtained in terms of the particle interaction strength, temperature and force distribution, in section 3 we will discuss how to calculate the relevant thermodynamic quantities, name...

Energetics of synchronization in coupled oscillators rotating on circular trajectories

“…(B1) now becomes the following phase equations corresponding to Eqs. (26) and (27) in the main text aṡ…”

“…In general, phase equations may be more complicated, where the natural frequency is phase-dependent and the coupling function is no longer the function of the phase difference (see Eqs. (26) and (27) below as an example). However, applying standard techniques in nonlinear dynamics such as cycle averaging under a suitable variable transformation, we can reduce such phase equations into the same form as Eqs.…”

“…Figure 2 (b) shows the G-dependence of the mean frequency Ω i obtained from the original dynamics given by Eqs. (26) and (27) and the cycle-averaged one given by …”

“…(26) and (27) with the variable φ i can be rewritten by using Φ i with the dynamics Eqs. (31) and (32) via the relatioṅ…”

“…To develop this energetics of synchronization, we need to unify energetic concepts usually treated in thermodynamics with the theory of coupled oscillators usually treated in nonlinear dynamics. Such a unification from the stochastic thermodynamics point of view [23,24] has been developed, in the analysis of collective dynamics based on a nonequilibrium equality [25] and in the optimization of the energy-conversion efficiency in all-to-all coupled many-oscillators systems [26].…”