We study the deternfinistic dynanfics of rotator chain with purely mechanical driving on the boundary by stability analysis and numerical sinmlation. Globally synchronous rotation, clustered synchronous rotation, and split synchronous rotation states are identified. In particular, we find that the single-peaked wariance distribution of angular momenta is the consequence of the deterministic dynamics. As a result, the operational definition of temperature used in the previous studies on rotator chain should be revisited.
A time-delayed feedback ratchet consisting of two Brownian particles interacting through the elastic spring is consid ered. The model describes the directed transport of coupled Brownian particles in an asymmetric two-well ratchet potential which can be calculated theoretically and implemented experimentally. We explore how the centre-of-mass velocity is af fected by the time delay, natural length of the spring, amplitude strength, angular frequency, external force, and the structure of the potential. It is found that the enhancement of the current can be obtained by varying the coupling strength of the delayed feedback system. When the thermal fluctuation and the harmonic potential match appropriately, directed current evolves periodically with the natural length of the spring and can achieve a higher transport coherence. Moreover, the external force and the amplitude strength can enhance the directed transport of coupled Brownian particles under certain conditions. It is expected that the polymer of large biological molecules may demonstrate a variety of novel cooperative effects in real propelling devices.
We investigate the free energy relation for a system contacting with a non-Markovian heat bath and find that the validity of the relation sensitively depends on the non-Markovian memory effect, which is especially related go the initial preparation effect. This memory effect drives the statistical distribution of the system out of the initial preparation, even if the system starts from an equilibrium state. This leads to the violation of the free energy relation. A possible way of eliminating this memory effect is proposed.
In this review, we give a retrospect of the recent progress in nonequilibrium statistical mechanics and thermodynamics in small dynamical systems. For systems with only a few number of particles, fluctuations and nonlinearity become sig- nificant and contribute to the nonequilibrium behaviors of the systems, hence the statistical properties and thermodynamics should be carefully studied. We review recent developments of this topic by starting from the Gallavotti-Cohen fluctuation theorem, and then to the Evans-Searles transient fluctuation theorem, Jarzynski free-energy equality, and the Crooks fluc- tuation relation. We also investigate the nonequilibrium free energy theorem for trajectories involving changes of the heat bath temperature and propose a generalized free-energy relation. It should be noticed that the non-Markovian property of the heat bath may lead to the violation of the free-energy relation.
In this review we investigate the rotation effect in the motion of coupled dimer in a two-dimensional asymmetric periodic potential. Free rotation does not generate directed transport in translational direction, while we find it plays an critical role in the motors motility when the dimer moves under the effect of asymmetry ratchet potential. In the presence of external force, we study the relation between the average current and the force numerically and theoretically. The numerical results show that only appropriate driving force could produce nonzero current and there are current transitions when the force is large enough. An analysis of stability analysis of limit cycles is applied to explain the occurrence of these transitions. Moreover, we numerically simulate the transport of this coupled dimer driven by the random fluctuations in the rotational direction. The existence of noise smooths the current transitions induced by the driving force and the resonance-like peaks which depend on the rod length emerge in small noise strength. Thanks to the noise in the rotational direction, autonomous motion emerges without the external force and large noise could make the current reversal happen. Eventually, the new mechanism to generate directed transport by the rotation is studied.
Dynamics of a one-dimensional array of non-locally coupled Kuramoto phase oscillators with an external potential is studied. A four-cluster chimera state is observed for the moderate strength of the external potential. Different from the clustered chimera states studied before, the instantaneous frequencies of the oscillators in a synchronized cluster are different in the presence of the external potential. As the strength of the external potential increases, a bifurcation from the two-cluster chimera state to the four-cluster chimera states can be found. These phenomena are well predicted analytically with the help of the Ott-Antonsen ansatz.
