31 research outputs found
Nonextensive Statistical Mechanics Application to Vibrational Dynamics of Protein Folding
The vibrational dynamics of protein folding is analyzed in the framework of
Tsallis thermostatistics. The generalized partition functions, internal
energies, free energies and temperature factor (or Debye-Waller factor) are
calculated. It has also been observed that the temperature factor is dependent
on the non-extensive parameter q which behaves like a scale parameter in the
harmonic oscillator model. As , we also show that these approximations
agree with the result of Gaussian network model.Comment: 8 pages, 2 figure
Quantum state-dependent diffusion and multiplicative noise: a microscopic approach
The state-dependent diffusion, which concerns the Brownian motion of a
particle in inhomogeneous media has been described phenomenologically in a
number of ways. Based on a system-reservoir nonlinear coupling model we present
a microscopic approach to quantum state-dependent diffusion and multiplicative
noise in terms of a quantum Markovian Langevin description and an associated
Fokker-Planck equation in position space in the overdamped limit. We examine
the thermodynamic consistency and explore the possibility of observing a
quantum current, a generic quantum effect, as a consequence of this
state-dependent diffusion similar to one proposed by B\"{u}ttiker [Z. Phys. B
{\bf 68}, 161 (1987)] in a classical context several years ago.Comment: To be published in Journal of Statistical Physics 28 pages, 3 figure
Thermodynamic Description of the Relaxation of Two-Dimensional Euler Turbulence Using Tsallis Statistics
Euler turbulence has been experimentally observed to relax to a
metaequilibrium state that does not maximize the Boltzmann entropy, but rather
seems to minimize enstrophy. We show that a recent generalization of
thermodynamics and statistics due to Tsallis is capable of explaining this
phenomenon in a natural way. The maximization of the generalized entropy
for this system leads to precisely the same profiles predicted by the
Restricted Minimum Enstrophy theory of Huang and Driscoll. This makes possible
the construction of a comprehensive thermodynamic description of Euler
turbulence.Comment: 15 pages, RevTe
An optimization principle for deriving nonequilibrium statistical models of Hamiltonian dynamics
A general method for deriving closed reduced models of Hamiltonian dynamical
systems is developed using techniques from optimization and statistical
estimation. As in standard projection operator methods, a set of resolved
variables is selected to capture the slow, macroscopic behavior of the system,
and the family of quasi-equilibrium probability densities on phase space
corresponding to these resolved variables is employed as a statistical model.
The macroscopic dynamics of the mean resolved variables is determined by
optimizing over paths of these probability densities. Specifically, a cost
function is introduced that quantifies the lack-of-fit of such paths to the
underlying microscopic dynamics; it is an ensemble-averaged, squared-norm of
the residual that results from submitting a path of trial densities to the
Liouville equation. The evolution of the macrostate is estimated by minimizing
the time integral of the cost function. The value function for this
optimization satisfies the associated Hamilton-Jacobi equation, and it
determines the optimal relation between the statistical parameters and the
irreversible fluxes of the resolved variables, thereby closing the reduced
dynamics. The resulting equations for the macroscopic variables have the
generic form of governing equations for nonequilibrium thermodynamics, and they
furnish a rational extension of the classical equations of linear irreversible
thermodynamics beyond the near-equilibrium regime. In particular, the value
function is a thermodynamic potential that extends the classical dissipation
function and supplies the nonlinear relation between thermodynamics forces and
fluxes
Some aspects of the Liouville equation in mathematical physics and statistical mechanics
This paper presents some mathematical aspects of Classical Liouville theorem
and we have noted some mathematical theorems about its initial value problem.
Furthermore, we have implied on the formal frame work of Stochastic Liouville
equation (SLE)
Recommended from our members
A computational model for viscous fluid flow, heat transfer, and melting in in situ vitrification melt pools
MAGMA is a FORTRAN computer code designed to viscous flow in in situ vitrification melt pools. It models three-dimensional, incompressible, viscous flow and heat transfer. The momentum equation is coupled to the temperature field through the buoyancy force terms arising from the Boussinesq approximation. All fluid properties, except density, are assumed variable. Density is assumed constant except in the buoyancy force terms in the momentum equation. A simple melting model based on the enthalpy method allows the study of the melt front progression and latent heat effects. An indirect addressing scheme used in the numerical solution of the momentum equation voids unnecessary calculations in cells devoid of liquid. Two-dimensional calculations can be performed using either rectangular or cylindrical coordinates, while three-dimensional calculations use rectangular coordinates. All derivatives are approximated by finite differences. The incompressible Navier-Stokes equations are solved using a new fully implicit iterative technique, while the energy equation is differenced explicitly in time. Spatial derivatives are written in conservative form using a uniform, rectangular, staggered mesh based on the marker and cell placement of variables. Convective terms are differenced using a weighted average of centered and donor cell differencing to ensure numerical stability. Complete descriptions of MAGMA governing equations, numerics, code structure, and code verification are provided. 14 refs