Engineering
81
en
research_article
false
1981-09-01
Nonequilibrium measures which exhibit a temperature gradient: Study of a model
1981-09
http://link.springer.com/10.1007/BF01941803
127-147
2019-04-11T11:13
articles
We give some rules to define measures which could describe heat flow in homogeneous crystals. We then study a particular model which is explicitly solvable: the one dimensional nearest neighborhood Ising model. We analyze two cases. In the first one the spins at the two boundaries interact with reservoirs at different temperatures; in the thermodynamical limit the measure we introduce converges locally to Gibbs measures and a temperature profile is so derived. We obtain an explicit expression for the thermal conductivity coefficient which depends on the temperature. In the second case we study the asymptotic behavior starting from an initial state in which each half of the space is at a different temperature. We find again a temperature profile which asymptotically obeys the heat equation with the thermal conductivity coefficient previously derived. From a mathematical point of view, the analysis of the invariant measure is made possible by studying a “time-reversed” process related to a graphical representation of an associated process. This provides us with an explicit formula for then-fold correlation function and we study the limiting behavior using both this representation (for proving an exchangeability result) and a Donsker-type, spacetime renormalization procedure.
https://scigraph.springernature.com/explorer/license/
1
fca5e568bcfc3c74ede3bf0450e926be5a4e6a0481f514b423915403f90437dd
readcube_id
C.
Kipnis
Dipartimento di Matematica, Libera Università di Trento, I-38050, Povo (Trento), Italy
Interdisciplinary Engineering
E.
Presutti
Centre de Mathématiques de l'Ecole Polytechnique, Plateau de Palaiseau, F-91128, Palaiseau Cedex, France
0010-3616
1432-0916
Communications in Mathematical Physics
doi
10.1007/bf01941803
pub.1053040699
dimensions_id
Springer Nature - SN SciGraph project
University of Sao Paulo
Instituto de Matématica e Estatistica, Universidade de São Paulo, São Paulo, Brazil
Marchioro
C.
Galves
A.
Istituto Matematico, Università di Roma, I-00100, Roma, Italy
Sapienza University of Rome