9,727 research outputs found
Local Detailed Balance : A Microscopic Derivation
Thermal contact is the archetype of non-equilibrium processes driven by
constant non-equilibrium constraints when the latter are enforced by reservoirs
exchanging conserved microscopic quantities. At a mesoscopic scale only the
energies of the macroscopic bodies are accessible together with the
configurations of the contact system. We consider a class of models where the
contact system, as well as macroscopic bodies, have a finite number of possible
configurations. The global system with only discrete degrees of freedom has no
microscopic Hamiltonian dynamics, but it is shown that, if the microscopic
dynamics is assumed to be deterministic and ergodic and to conserve energy
according to some specific pattern, and if the mesoscopic evolution of the
global system is approximated by a Markov process as closely as possible, then
the mesoscopic transition rates obey three constraints. In the limit where
macroscopic bodies can be considered as reservoirs at thermodynamic equilibrium
(but with different intensive parameters) the mesoscopic transition rates turn
into transition rates for the contact system and the third constraint becomes
local detailed balance ; the latter is generically expressed in terms of the
microscopic exchange entropy variation, namely the opposite of the variation of
the thermodynamic entropy of the reservoir involved in a given microscopic jump
of the contact system configuration. For a finite-time evolution after contact
has been switched on we derive a fluctuation relation for the joint probability
of the heat amounts received from the various reservoirs. The generalization to
systems exchanging energy, volume and matter with several reservoirs, with a
possible conservative external force acting on the contact system, is given
explicitly.Comment: 26 pages. arXiv admin note: substantial text overlap with
arXiv:1302.453
On the nonequilibrium entropy of large and small systems
Thermodynamics makes definite predictions about the thermal behavior of
macroscopic systems in and out of equilibrium. Statistical mechanics aims to
derive this behavior from the dynamics and statistics of the atoms and
molecules making up these systems. A key element in this derivation is the
large number of microscopic degrees of freedom of macroscopic systems.
Therefore, the extension of thermodynamic concepts, such as entropy, to small
(nano) systems raises many questions. Here we shall reexamine various
definitions of entropy for nonequilibrium systems, large and small. These
include thermodynamic (hydrodynamic), Boltzmann, and Gibbs-Shannon entropies.
We shall argue that, despite its common use, the last is not an appropriate
physical entropy for such systems, either isolated or in contact with thermal
reservoirs: physical entropies should depend on the microstate of the system,
not on a subjective probability distribution. To square this point of view with
experimental results of Bechhoefer we shall argue that the Gibbs-Shannon
entropy of a nano particle in a thermal fluid should be interpreted as the
Boltzmann entropy of a dilute gas of Brownian particles in the fluid
Heat Transport in Quantum Spin Chains: Stochastic Baths vs Quantum Trajectories
We discuss the problem of heat conduction in quantum spin chain models. To
investigate this problem it is necessary to consider the finite open system
connected to heat baths. We describe two different procedures to couple the
system with the reservoirs: a model of stochastic heat baths and the quantum
trajectories solution of the quantum master equation. The stochastic heat bath
procedure operates on the pure wave function of the isolated system, so that it
is locally and periodically collapsed to a quantum state consistent with a
boundary nonequilibrium state. In contrast, the quantum trajectories procedure
evaluates ensemble averages in terms of the reduced density matrix operator of
the system. We apply these procedures to different models of quantum spin
chains and numerically show their applicability to study the heat flow.Comment: 13 pages, 5 figures, submitted to European Physics Journal Special
Topic
Transport Phenomena at a Critical Point -- Thermal Conduction in the Creutz Cellular Automaton --
Nature of energy transport around a critical point is studied in the Creutz
cellular automaton. Fourier heat law is confirmed to hold in this model by a
direct measurement of heat flow under a temperature gradient. The thermal
conductivity is carefully investigated near the phase transition by the use of
the Kubo formula. As the result, the thermal conductivity is found to take a
finite value at the critical point contrary to some previous works. Equal-time
correlation of the heat flow is also analyzed by a mean-field type
approximation to investigate the temperature dependence of thermal
conductivity. A variant of the Creutz cellular automaton called the Q2R is also
investigated and similar results are obtained.Comment: 27 pages including 14figure
A Symmetry Property of Momentum Distribution Functions in the Nonequilibrium Steady State of Lattice Thermal Conduction
We study a symmetry property of momentum distribution functions in the steady
state of heat conduction. When the equation of motion is symmetric under change
of signs for all dynamical variables, the distribution function is also
symmetric. This symmetry can be broken by introduction of an asymmetric term in
the interaction potential or the on-site potential, or employing the thermal
walls as heat reservoirs. We numerically find differences of behavior of the
models with and without the on-site potential.Comment: 13 pages. submitted to JPS
- …