### Citations

612 |
Non-equilibrium Thermodynamics
- Groot, Mazur
- 1984
(Show Context)
Citation Context ...ecome ju =−D∇(cT )+ vcT (3.12a) jρ =−D∇c + vc. (3.12b) These should be compared with ju = L11∇(1/T )+ L12∇(−µ/T ) (3.13a) jρ = L21∇(1/T )+ L22∇(−µ/T ) (3.13b) from the theory of linear thermodynamics =-=[20, 22]-=-. Using (3.2) and (3.3), we obtain ju =−L11(∇T )/T 2 + L12 [(∇T )/T − (∇c)/c + ∇ν] (3.14a) jρ =−L21(∇T )/T 2 + L22 [(∇T )/T − (∇c)/c + ∇ν]. (3.14b) Setting ∇T = ∇c = 0, we find L12∇ν = vcT and L22∇ν =... |

528 |
Thermodynamics and an Introduction to Thermostatistics;
- Callen
- 1985
(Show Context)
Citation Context ...h it may vary from one site to another (see Appendix). Having the fundamental relation (3.1), we can proceed to obtain the equations of state for the intensive variables in the entropy representation =-=[20]-=-: 1 Ti = ( ∂Si ∂Ei ) Ni = ni Ei (3.2) and −µi Ti = ( ∂Si ∂Ni ) Ei = ln ( Ei n2i ) + νi, (3.3) Long-range correlations in coupled transport 6 where νi := si−2 is a constant, which again may have differ... |

125 | Fourier’s law: A challenge to theorists,”
- Bonetto, Lebowitz, et al.
- 2000
(Show Context)
Citation Context ...ation of macroscopic transport laws, such as Fourier’s law of heat conduction, from microscopic dynamics, for systems which are maintained out of equilibrium by the imposition of thermodynamic fluxes =-=[1, 2, 3]-=-. For certain classes of stochastic mass-transport equations, known as zero-range processes, in which the dynamics of mass leaving a site depends only on the occupation number at that site, the statio... |

121 |
Thermal Conduction in Classical Low-Dimensional Lattices.
- Lepri, Livi, et al.
- 2003
(Show Context)
Citation Context ...ation of macroscopic transport laws, such as Fourier’s law of heat conduction, from microscopic dynamics, for systems which are maintained out of equilibrium by the imposition of thermodynamic fluxes =-=[1, 2, 3]-=-. For certain classes of stochastic mass-transport equations, known as zero-range processes, in which the dynamics of mass leaving a site depends only on the occupation number at that site, the statio... |

115 |
A Modern Course in Statistical Physics,
- Reichl
- 1980
(Show Context)
Citation Context ...he quotient of the number of states consistent with these requirements over the total number of states available to the system. These numbers are proportional to the corresponding structure functions =-=[24]-=-, given by ω(E,N,V ) := ∫ δ (HN(p,q)−E) dpdq, (A.1) where HN(p,q) is the N-particle Hamiltonian describing the dynamics at each site, and the integration is carried out over the phase space of the N p... |

89 |
Non-equilibrium steady states: fluctuations and large deviations of the density and of the current,
- Derrida
- 2007
(Show Context)
Citation Context ...th exclusion [9] [10], and lattice-gas cellular automata [11]. Also, exact results for all correlation functions were found using matrix technique for the symmetric simple exclusion process: see e.g. =-=[12]-=- for a recent review, where the relation of long-range correlations to a non-local free energy functional is also discussed. An approximation of the invariant measure using Gaussians in a suitably rot... |

75 |
Long range correlations for stochastic lattice gases in a non-equilibrium steady state,
- Spohn
- 1983
(Show Context)
Citation Context ...stationary states have already been studied in many simple models, including a stochastic master equation describing heat flow [7], oscillators which exchange energy [8], lattice-gases with exclusion =-=[9]-=- [10], and lattice-gas cellular automata [11]. Also, exact results for all correlation functions were found using matrix technique for the symmetric simple exclusion process: see e.g. [12] for a recen... |

49 |
Heat flow in an exactly solvable model,
- Kipnis, Marchioro, et al.
- 1982
(Show Context)
Citation Context ...lations arising in nonequilibrium stationary states have already been studied in many simple models, including a stochastic master equation describing heat flow [7], oscillators which exchange energy =-=[8]-=-, lattice-gases with exclusion [9] [10], and lattice-gas cellular automata [11]. Also, exact results for all correlation functions were found using matrix technique for the symmetric simple exclusion ... |

33 |
Nonequilibrium energy profiles for a class of 1-D models.
- Eckmann, Young
- 2006
(Show Context)
Citation Context ...y Suárez et al. [11], for the case where transport is by particles with exclusion, but with a single conserved quantity. In particular, long-range correlations in the so-called “random-halves” model =-=[15]-=- of coupled matter and heat transport were recently studied in [16], principally heuristically and numerically. The model we study in this paper can be considered to be a simplified version of the ran... |

25 |
Transport properties of a modified Lorentz gas
- Larralde, Leyvraz, et al.
- 2003
(Show Context)
Citation Context ...oned above, our model is related to the recently-introduced random-halves model [15, 16], designed to model, rather faithfully, the Hamiltonian dynamics underlying the transport phenomena observed in =-=[17, 18]-=-. In the random-halves model, each particle jumps to a neighbouring site with a rate which is proportional to the square root of its kinetic energy, and which is a factor δ times the rate at which a p... |

23 | Coupled Normal Heat and Matter Transport in a Simple Model System - Meja-Monasterio, Larralde, et al. |

18 |
Temperature profiles in hamiltonian heat conduction
- Eckmann, Young
- 2004
(Show Context)
Citation Context ...fined concentration and mean energy profiles, ρi and 〈Ei〉, as a function of the position i in the system. Related profiles have been studied in detail for random-halves and other stochastic models in =-=[15, 21]-=-. The transport equations can be easily derived by recalling that the total energy Ei at site i at time t + 1 is given by the energy ei that was there at time t, plus the energy brought in by the walk... |

17 |
Expression for the stationary distribution in nonequilibrium steady states
- Komatsu, Kakagawa
(Show Context)
Citation Context ...ation of macroscopic transport laws, such as Fourier’s law of heat conduction, from microscopic dynamics, for systems which are maintained out of equilibrium by the imposition of thermodynamic fluxes =-=[1, 2, 3]-=-. For certain classes of stochastic mass-transport equations, known as zero-range processes, in which the dynamics of mass leaving a site depends only on the occupation number at that site, the statio... |

17 |
Generic long-range correlations in molecular fluids,
- Dorfman, Kirkpatrick, et al.
- 1994
(Show Context)
Citation Context ...on of these systems. Furthermore, the fact that the distribution does not factorise implies the existence of spatial correlations between different sites, as has been discussed in many previous works =-=[5, 6]-=-. These spatial correlations in nonequilibrium states have been studied at a mescoscopic level using fluctuating hydrodynamics [6]. Generically, they tend to be long-range, spanning the whole length o... |

12 |
Factorized steady states in mass transport models
- Evans, Majumdar, et al.
- 2004
(Show Context)
Citation Context ...mber at that site, the stationary-state distribution is known to factorise into the product of single-site distributions under certain conditions, which enables many analytical results to be obtained =-=[4]-=-. However, for more complicated models, this distribution no longer factorises. In this case, the appropriate characterisation of the stationary-state distribution becomes a central goal for the descr... |

10 |
Long-range correlations for conservative dynamics
- Garrido, Lebowitz, et al.
- 1990
(Show Context)
Citation Context ...ionary states have already been studied in many simple models, including a stochastic master equation describing heat flow [7], oscillators which exchange energy [8], lattice-gases with exclusion [9] =-=[10]-=-, and lattice-gas cellular automata [11]. Also, exact results for all correlation functions were found using matrix technique for the symmetric simple exclusion process: see e.g. [12] for a recent rev... |

9 |
A stochastic model of anomalous heat transport: analytical solution of the nonequilibrium steady state
- Lepri, Mejı́a-Monasterio, et al.
(Show Context)
Citation Context ...ange correlations to a non-local free energy functional is also discussed. An approximation of the invariant measure using Gaussians in a suitably rotated coordinate system has recently been obtained =-=[13, 14]-=-; and related analytical results were previously found by Suárez et al. [11], for the case where transport is by particles with exclusion, but with a single conserved quantity. In particular, long-ra... |

8 |
Nonequilibrium Invariant Measure under Heat
- Delfini, Lepri, et al.
- 2008
(Show Context)
Citation Context ...ange correlations to a non-local free energy functional is also discussed. An approximation of the invariant measure using Gaussians in a suitably rotated coordinate system has recently been obtained =-=[13, 14]-=-; and related analytical results were previously found by Suárez et al. [11], for the case where transport is by particles with exclusion, but with a single conserved quantity. In particular, long-ra... |

6 |
Onset of spatial correlations in nonequilibrium systems: a master-equation description” Phys
- G, Mansour
- 1984
(Show Context)
Citation Context ... a microscopic point of view, the correlations arising in nonequilibrium stationary states have already been studied in many simple models, including a stochastic master equation describing heat flow =-=[7]-=-, oscillators which exchange energy [8], lattice-gases with exclusion [9] [10], and lattice-gas cellular automata [11]. Also, exact results for all correlation functions were found using matrix techni... |

5 | Correlations in nonequilibrium steady states of random halves models
- Lin, Young
- 2007
(Show Context)
Citation Context ... with exclusion, but with a single conserved quantity. In particular, long-range correlations in the so-called “random-halves” model [15] of coupled matter and heat transport were recently studied in =-=[16]-=-, principally heuristically and numerically. The model we study in this paper can be considered to be a simplified version of the random-halves model, still containing two explicitly conserved quantit... |

4 |
Local thermodynamic equilibrium for some stochastic models of Hamiltonian origin
- Ravishankar, Young
(Show Context)
Citation Context ...range correlations in coupled transport 10 has recently been proved correct for the random-halves model, in the limit when the number of sites goes to ∞, so that the temperature gradient goes to zero =-=[23]-=-. Under the hypothesis of local thermodynamic equilibrium, we can use (2.7) to calculate κi = 〈 E2i /(mi + 1) 〉 , obtaining κi = ρi β 2i = ρiT 2i . (4.15) We will use this approximate analytical form ... |

3 |
Long-range correlations in nonequilibrium systems: Lattice gas automaton approach
- Suárez, Boon, et al.
- 1996
(Show Context)
Citation Context ...in many simple models, including a stochastic master equation describing heat flow [7], oscillators which exchange energy [8], lattice-gases with exclusion [9] [10], and lattice-gas cellular automata =-=[11]-=-. Also, exact results for all correlation functions were found using matrix technique for the symmetric simple exclusion process: see e.g. [12] for a recent review, where the relation of long-range co... |

1 |
Reséndiz Antonio and Hernán Larralde. The statistics of diffusive flux
- Margarita
- 2005
(Show Context)
Citation Context ...impler expressions (than, say, 1 or 3 dimensional ideal gases) and is closer to the intrinsic 2-dimensional nature of various previous models for coupled transport. 2.2. Equilibrium state It is known =-=[19]-=- that many non-interacting walkers, even when subjected to a density gradient, attain a stationary state which factorises: the probability of having occupation numbers n := (n1, . . . ,nL) is given by... |