The generalized Kramers theory for nonequilibrium open one-dimensional systems

Abstract

The Kramers' theory of activated processes is generalized for nonequilibrium open one-dimensional systems. We consider both the internal noise due to thermal bath and the external noise which are stationary, Gaussian and are characterized by arbitrary decaying correlation functions. We stress the role of a nonequilibrium stationary state distribution for this open system which is reminiscent of an equilibrium Boltzmann distribution in calculation of rate.The generalized rate expression we derive here reduces to the specific limiting cases pertaining to the closed and open systems for thermal and non-thermal steady state activation processes. PACS number(s) : 02.50.Ey, 05.70.Ln, Typeset using REVT E X 1

Generalization of the escape rate from a metastable state driven by external cross-correlated noise processes

“…In absence of FDR, such external input of energy makes the system open and in contrast to the closed system the equilibrium Boltzmann distribution gets replaced by a steady state distribution (SSD) in the long time limit. It may therefore be anticipated that the absence of FDR tends to make the SSD function dependent on the strength and correlation time of external noise as well as on the dissipation of the system [14,15,16]. It is pertinent to point out that though thermodynamically closed systems with homogeneous boundary conditions possess, in general, time-dependent solution, the driven open systems may settle down to complicated multiple steady states when one takes into account nonlinearity of the systems.…”

“…In nonequilibrium statistical mechanical terminology, such systems are referred to as closed system [12]. It may happen sometime that an additional source of energy in the form of fluctuations can be pumped from outside for * Electronic address: jprc˙8@yahoo.com † Electronic address: sudip˙chattopadhyay@rediffmail.com ‡ Electronic address: skbanik@phys.vt.edu which there is no counter balancing force like dissipation [13,14,15,16]. In absence of FDR, such external input of energy makes the system open and in contrast to the closed system the equilibrium Boltzmann distribution gets replaced by a steady state distribution (SSD) in the long time limit.…”

Analytical and numerical investigation of escape rate for a noise driven bath

“…After making use of the appropriate transformations and boundary conditions for reduced distribution functions [7] we obtain the barrier crossing rate k given by…”

“…Since then the model and several of its variants have been ubiquitous in many areas of physics, chemistry and biology for understanding the nature of activated processes in classical [2][3][4][5][6][7], quantum and semiclassical [8][9][10][11] systems, in general. These have become the subject of several reviews [12][13][14] and monograph [15] in the recent past.…”

Quantum phase-space function formulation of reactive flux theory

“…Over the decades the field has grown in various new directions, e.g. , extension of Kramers results to non-Markovian regime 4,5,6 , generalizations to higher dimensions 7,8 , inclusion of complex potentials 9,10 , generalization to open systems 11,12,13 , analysis of semiclassical and quantum effects 14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29 , thermal ratchet 30 and molecular motors 31 etc. These developments have been the subject of several reviews and monographs.We refer to 15,16,17,22 .…”