arXiv subjects

Hans Christian Ottinger

Publications and source records attributed to Hans Christian Ottinger.

4 recordsLinked to original sources

arXiv2010

Probing a critical length scale at the glass transition

We give evidence of a clear structural signature of the glass transition, in terms of a static correlation length with the same dependence on the system size which is typical of critical phenomena. Our approach is to introduce an external, static perturbation to extract the structural information from the system's response. In particular, we consider the transformation behavior of the local minima of the underlying potential energy landscape (inherent structures), under a static deformation. The finite-size scaling analysis of our numerical results indicate that the correlation length diverges at a temperature $T_c$, below the temperatures here the system can be equilibrated. Our numerical results are consistent with random first order theory, which predicts such a divergence with a critical exponent $ν=2/3$ at the Kauzmann temperature, where the extrapolated configurational entropy vanishes.

cond-mat.stat-mech↗

arXiv2009

Nonequilibrium Thermodynamics of the First and Second Kind: Averages and Fluctuations

We compare two approaches to nonequilibrium thermodynamics, the two-generator bracket formulation of time-evolution equations for averages and the macroscopic fluctuation theory, for an isothermal driven diffusive system under steady state conditions. The fluctuation dissipation relations of both approaches play an important role for a detailed comparison. The nonequilibrium Helmholtz free energies introduced in these two approaches differ as a result of boundary conditions. A Fokker-Planck equation derived by projection operator techniques properly reproduces long range fluctuations in nonequilibrium steady states and offers the most promising possibility to describe the physically relevant fluctuations around macroscopic averages for time-dependent nonequilibrium systems.

cond-mat.stat-mech↗

arXiv2003

Irreversibility in the short memory approximation

A recently introduced systematic approach to derivations of the macroscopic dynamics from the underlying microscopic equations of motions in the short-memory approximation [Gorban et al, Phys. Rev. E, 63, 066124 (2001)] is presented in detail. The essence of this method is a consistent implementation of Ehrenfest's idea of coarse-graining, realized via a matched expansion of both the microscopic and the macroscopic motions. Applications of this method to a derivation of the nonlinear Vlasov-Fokker-Planck equation, diffusion equation and hydrodynamic equations of the fluid with a long-range mean field interaction are presented in full detail. The advantage of the method is illustrated by the computation of the post-Navier-Stokes approximation of the hydrodynamics which is shown to be stable unlike the Burnett hydrodynamics.

cond-mat.stat-mech↗

arXiv2002

The additive generalization of the Boltzmann entropy

There exists only one generalization of the classical Boltzmann-Gibbs-Shannon entropy functional to a one-parametric family of additive entropy functionals. We find analytical solution to the corresponding extension of the classical ensembles, and discuss in some detail the example of the deformation of the uncorrelated state.

cond-mat.stat-mech↗