Integrable heat conduction model

Abstract

We consider a stochastic process of heat conduction where energy is redistributed along a chain between nearest neighbor sites via an improper beta distribution. Similar to the well-known Kipnis–Marchioro–Presutti (KMP) model, the finite chain is coupled at its ends with two reservoirs that break the conservation of energy when working at different temperatures. At variance with KMP, the model considered here is integrable, and one can write in a closed form the n-point correlation functions of the non-equilibrium steady state. As a consequence of the exact solution one, can directly prove that the system is in “local equilibrium,” which is described at the macro-scale by a product measure. Integrability manifests itself through the description of the model via the open Heisenberg chain with non-compact spins. The algebraic formulation of the model allows us to interpret its duality relation with a purely absorbing particle system as a change of representation.

Close-to-equilibrium heat capacity

“…. , N}, [20,21]. Each end is imagined connected to a thermal bath but at a different temperature, left and right.…”

Duality for a boundary driven asymmetric model of energy transport

“…Not long ago two new models belonging to this class have been introduced in [17] via integrable non-compact spin chains and their duality relation shown in [16,18]. For these new models formulae for the non-equilibrium steady states were obtained in [16,19].…”

“…Not long ago two new models belonging to this class have been introduced in [17] via integrable non-compact spin chains and their duality relation shown in [16,18]. For these new models formulae for the non-equilibrium steady states were obtained in [16,19]. A characterization of these measures as mixture products of inhomogeneous distributions has been revealed in [6,7], however for an asymmetric dynamics this characterization is still an open problem.…”