Detailed Balance

Reconstruction of equations of motion from incomplete or noisy data and dimension reduction are two fundamental problems in the study of dynamical systems with many degrees of freedom. For the latter, extensive efforts have been made, but with limited success, to generalize the Zwanzig–Mori projection formalism, originally developed for Hamiltonian systems close to thermodynamic equilibrium, to general non-Hamiltonian systems lacking detailed balance. One difficulty introduced by such systems is the lack of an invariant measure, needed to define a statistical distribution. Based on a recent discovery that a non-Hamiltonian system defined by a set of stochastic differential
equations can be mapped to a Hamiltonian system, we develop such general projection formalism. In the resulting generalized Langevin equations, a set of generalized fluctuation–dissipation relations connect the memory kernel and the random noise terms, analogous to Hamiltonian systems obeying detailed balance. Lacking of these relations restricts previous application of the generalized Langevin formalism. Result of this work may serve as the theoretical basis for further technical developments
on model reconstruction with reduced degrees of freedom. We first use an analytically solvable example to illustrate the formalism and the fluctuation–dissipation relation. Our numerical test on a chemical network with end-product inhibition further demonstrates the validity of the formalism. We suggest that the formalism can find wide applications in scientific modeling. Specifically, we discuss potential applications to biological networks. In particular, the method provides a suitable framework for gaining insights into network properties such as robustness and parameter transferability

The derivation of Casimir forces between dielectrics can be simplified by ignoring absorption, calculating energy changes due to displacements of the dielectrics, and only then admitting absorption by allowing permittivities to be complex. As a first step towards a better understanding of this situation we consider in this paper the model of a dielectric as a collection of oscillators, each of which is coupled to a reservoir giving rise to damping and Langevin forces on the oscillators and a noise polarization acting as a source of a fluctuating electromagnetic (EM) field in the dielectric. The model leads naturally to expressions for the quantized EM fields that are consistent with those obtained by different approaches, and also results in a fluctuation-dissipation relation between the noise polarization and the imaginary part of the permittivity. Our main result is the derivation of an expression for the QED energy density of a uniform dispersive, absorbing media in thermal equil...

This paper discusses the possibility of manufacturing the intermediate band solar cell (IBSC), a cell with the potential of achieving 63.2% of efficiency under concentrated sunlight, using quantum dot technology. The 0-dimensionality nature of the dots avoids electron thermalisation between bands enhancing the possibilities for radiative recombination between bands and making possible the existence of three quasi-fermi levels, some of the pivots the theory of the IBSC is sustained on. In this sense, it is suggested that an InGaAs/AlGaAs system could be used for band engineering the optimum bandgaps of the IBSC cell (0.71 and 1.24 eV). Dots should be about 40 Å of radius, spaced in the range of 100 Å and distributed in a three dimensional array. The Stranski and Krastanow method is proposed as a technology for achieving this goal. The possibility of n-doping the dots is also discussed

In the present chapter we will discuss the creation of surface supported metal clusters through nucleation and growth in Molecular Beam Epitaxy (MBE). MBE is commonly used to grow thin epitaxial films from the vapour phase onto single crystal substrates under ultra-high vacuum (UHV) conditions [1]. In thin film growth the nucleation of stable clusters is the preliminary step to the immobilisation and further condensation of film atoms or molecules. If one is close to thermodynamic equilibrium it is irrelevant how and where this nucleation takes place and the film topography is given by the balance of the free energies of film surface, substrate surface, and the interface between the two [2]. However, the prerequisite to the growth is to be away from thermodynamic equilibrium, at least to some extent, since detailed balance arguments require that in equilibrium all processes appear with equal rates, including condensation and desorption. Therefore, the entire growth system hardly ado...

Dual phospho/dephosphorylation cycles, as well as covalent enzymatic-catalyzed modifications of substrates, are widely diffused within cellular systems and are crucial for the control of complex responses such as learning, memory and cellular fate determination. Despite the large body of deterministic studies and the increasing work aimed to elucidate the effect of noise in such systems, some aspects remain unclear. Here we study the stationary distribution provided by the two-dimensional Chemical Master Equation for a well known model of a two step phospho/dephosphorylation cycle using the quasi steady state approximation of the enzymatic kinetics. Our aim is to analyze the role of fluctuations and the molecules distribution properties in the transition to a bistable regime. When detailed balance conditions are satisfied it is possible to compute equilibrium distributions in a closed and explicit form. When detailed balance is not satisfied, the stationary non-equilibrium state is strongly influenced by the chemical fluxes. In the last case, we show how the Helmholtz decomposition of the external field associated to the generation and recombination transition rates, into a conservative and a rotational (irreversible) part, allows to compute the stationary distribution via a perturbative approach . For a finite number of molecules, there exists diffusion dynamics in a macroscopic region of the state space, where a relevant transition rate between the two critical points is observed. Further, the stationary distribution function can be approximated by the solution of a Fokker-Planck equation. We illustrate the theoretical results using several numerical simulations.