Statistical-Mechanical Theory of Random Frequency Modulations and Generalized Brownian Motions

Tokuyama, Michio; Mori, H.

doi:10.1143/ptp.55.411

Cited by 237 publications

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“…(8) contains the dissipative part due to the exciton-vibrational (Chl-protein) coupling. We use the partial ordering prescription (POP) theory (Mukamel et al, 1978;Tokuyama and Mori, 1976;Renger and Marcus, 2002a;Richter et al, 2006;Renger et al, 2007) to obtain this part, since it was demonstrated to be the most accurate one for the present type of system (Renger and Marcus, 2002a;Renger et al, 2007).…”

Section: Description Of Linear Optical Spectramentioning

confidence: 99%

How the molecular structure determines the flow of excitation energy in plant light-harvesting complex II

Renger

Madjet

Knorr

et al. 2011

Journal of Plant Physiology

157

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Section: Description Of Linear Optical Spectramentioning

confidence: 99%

How the molecular structure determines the flow of excitation energy in plant light-harvesting complex II

Renger

Madjet

Knorr

et al. 2011

Journal of Plant Physiology

157

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“…This yields the memory term (time convolution) in equation (2.5). Tokuyama & Mori [35] have shown how the NZ-PDF equation (2.5) can be transformed into a time-convolutionless form, thus avoiding, at least formally, the memory term. This matter was further discussed by several authors [36][37][38].…”

Section: Nakajima-zwanzig Projection Operator Frameworkmentioning

confidence: 99%

Convolutionless Nakajima–Zwanzig equations for stochastic analysis in nonlinear dynamical systems

Venturi

Karniadakis

2014

Proc. R. Soc. A.

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Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima-Zwanzig-Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection-reaction problems.

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“…In order to avoid unnecessary technical complications, we have avoided time-convolution meth-ods. From mutually equivalent time-convolutionless methods, we have chosen (like in [3]) that of Tokuyama and Mori [11]. In order to avoid unnecessary discussions about role of approximations, we have employed one of the scaling procedures turning, in the limiting sense, Tokuyama-Mori equations into exact kinetic equations.…”

Section: Equations Of Motionmentioning

confidence: 99%

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Čápek

Bok

1999

Czechoslovak Journal of Physics

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A previously published model of the isothermal Maxwell demon as one of models of open quantum systems endowed with faculty of selforganization is reconstructed here. It describes an open quantum system interacting with a single thermodynamic bath but otherwise not aided from outside. Its activity is given by the standard linear Liouville equation for the system and bath. Owing to its selforganization property, the model then yields cyclic conversion of heat from the bath into mechanical work without compensation. Hence, it provides an explicit thought construction of perpetuum mobile of the second kind, contradicting thus the Thomson formulation of the second law of thermodynamics. No approximation is involved as a special scaling procedure is used which makes the kinetic equations employed exact. IntroductionIn this letter, we should like to report on a result which can be obtained, for the model in question, without approximations from standard quantum theory of open systems governed by the linear Liouville -von Neumann equation. Irrespective of this, it contradicts the second law of thermodynamics. Leaving details of physical motivation to a next publication, we mention here just the fact that the main inspiration for construction of the model has been taken from biology, namely from topological changes of biologically important molecules upon detecting, at a specific site (receptor), particles (excitations, molecules or molecular groups) to be processed [1].Previous version of the model has been published in [2]. Detailed treatment of this model [3] as well as other microscopic models of open quantum systems working on analogous principles [4,5,6,7,8] revealed property of spontaneous (i.e. not induced by external flows) selforganization. This then leads to such unexpected phenomena contradicting basic principles of statistical thermodynamics as, e.g., violation of consequences of the detailed balance (in connection with impossibility of rigorous justification thereof). From this, implicit violations of the second law of thermodynamics could be deduced as mentioned in, e.g., [5,6]. Here, we reconstruct the model so that it is able to work cyclically and without compensation as a perpetuum mobile of the second kind, in the sense contradicting explicitly the Thomson formulation of the second law of thermodynamics [9]. ModelThe fully quantum Hamiltonian of our model in its simplest version (see also [10]) can be as usual written as a sum of the Hamiltonians of the (extended) system, thermodynamic bath, and that of the system-bath interaction. Thus,

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Statistical-Mechanical Theory of Random Frequency Modulations and Generalized Brownian Motions

Cited by 237 publications

References 0 publications

How the molecular structure determines the flow of excitation energy in plant light-harvesting complex II

How the molecular structure determines the flow of excitation energy in plant light-harvesting complex II

Convolutionless Nakajima–Zwanzig equations for stochastic analysis in nonlinear dynamical systems

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