A Low Temperature Analysis of the Boundary Driven Kawasaki Process
- PDF / 673,587 Bytes
- 17 Pages / 439.37 x 666.142 pts Page_size
- 71 Downloads / 137 Views
A Low Temperature Analysis of the Boundary Driven Kawasaki Process Christian Maes · Winny O’Kelly de Galway
Received: 5 June 2013 / Accepted: 23 October 2013 / Published online: 12 November 2013 © Springer Science+Business Media New York 2013
Abstract Low temperature analysis of nonequilibrium systems requires finding the states with the longest lifetime and that are most accessible from other states. We determine these dominant states for a one-dimensional diffusive lattice gas subject to exclusion and with nearest neighbor interaction. They do not correspond to lowest energy configurations even though the particle current tends to zero as the temperature reaches zero. That is because the dynamical activity that sets the effective time scale, also goes to zero with temperature. The result is a non-trivial asymptotic phase diagram, which crucially depends on the interaction coupling and the relative chemical potentials of the reservoirs. Keywords Nonequilibrium dynamics
1 Introduction The characterization of a macroscopic system of fixed volume and in thermodynamic equilibrium with a unique heat bath at a given temperature and chemical potential proceeds from the study of its (grand-canonical) free energy functional. At low temperatures energy considerations dominate and the phase diagram starts from identifying the ground states upon which small thermal excitations are built and entropic considerations enter. For equilibrium circumstances then, following the important work in equilibrium statistical mechanics around 1960–1990, a systematic low temperature analysis has evolved into a constructive tool, establishing phase transitions and enabling characterizations of low temperature phases; see [4, 9–11, 20, 21, 24] for some few pioneering examples in the mathematical physics literature. In contrast, low temperature analysis for nonequilibrium systems is virtually nonexistent, at least from a global perspective. Much has of course to do with the lack of general principles and with the great mathematical difficulties in treating spatially extensive
B
C. Maes · W. O’Kelly de Galway ( ) Instituut voor Theoretische Fysica, KU Leuven, Leuven, Belgium e-mail: [email protected]
992
C. Maes, W. O’Kelly de Galway
processes under steady nonequilibrium driving. Recent years have however seen various exactly solvable nonequilibrium processes very much including some driven diffusive lattice gases [6, 7, 15, 25, 26], and various ideas have been launched on the relevant large deviation theory for nonequilibria. In particular, a low temperature analysis for stochastic processes is mathematically very close to what is done in Freidlin-Wentzel theory for random perturbations of deterministic dynamics. One must simply add the nonequilibrium physics and the relevant examples. That was part of the recent paper [16], where a scheme was put forward to characterize the low temperature asymptotics of continuous time jump processes under the condition of local detailed balance. The present paper starts from that sa
Data Loading...
