Nonequilibrium phase transition in the case of correlated noises

Transitions and transport for a spatially periodic stochastic system with locally coupled oscillators

“…Another is the "Brownian motor," wherein for Brownian motion in stochastic spatial periodic potentials the spatial asymmetry or noise asymmetry leads to a systematic transport whose magnitude and even direction can be turned by the parameters of the noise [3,4]. A third is the nonequilibrium transition for a system with finitely or infinitely coupled oscillators, which is probably a phase transition (first or second order) [5][6][7][8][9][10] or is not [10,11]. For these systems, the most exciting factor is that a reentrant second-order phase transition was found for a general spatially extended model by Van den Broeck et al [6].…”

Effects of Gaussian colored noise on time evolution of information entropy in a damped harmonic oscillator

“…It is well known that the nature of random force (e.g. noise) may influence the dynamical systems in many aspects, such as stationary probability [7][8][9], escape rate [9,10], noise-induced phase transitions [11,12], stochastic resonance [4,5,[13][14][15] and the time derivative of information entropy [6,[16][17][18][19][20][21][22][23]. The specific nature of the stochastic process may play an important role in the process of equilibration for a given non-equilibrium state of the noise-driven dynamical system.…”

Nonequilibrium stochastic processes: Time dependence of entropy flux and entropy production

“…(13) implies that the first term has no definite sign while the second term is positive definitely since D s is always positive. Then one can identify the first and the second terms as entropy flux (Ṡ F ) and entropy production (Ṡ P ), respectively.…”

“…The aim of the present paper is to enquire in this connection about the imprints of color [12], white and cross-correlated noise processes [13,14] on time dependence of entropy, entropy production and entropy flux using a connection between the information entropy and the probability distribution function of the phase space variables for thermodynamically open systems. Based on a Fokker-Planck description of stochastic processes and the entropy balance equation we first consider here the relaxation of a dissipative dynamical system in presence of the noise processes to a steady state from a given nonequilibrium state in terms of thermodynamically inspired quantities.…”