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We describe a method, based on hard contact topology, of showing the existence of semi-infinite trajectories of contact Hamiltonian flows which start on one Legendrian submanifold and asymptotically converge to another Legendrian submanifold. We discuss a mathematical model of non-equilibrium thermodynamics where such trajectories play a role of relaxation processes, and illustrate our results in the case of the Glauber dynamics for the mean field Ising model.
In the setting of the principle of local equilibrium which asserts that the temperature is a function of the energy levels of the system, we exhibit plenty of steady states describing the condensation of free Bosons which are not in thermal equilibri
Metriplectic systems are state space formulations that have become well-known under the acronym GENERIC. In this work we present a GENERIC based state space formulation in an operator setting that encodes a weak-formulation of the field equations des
We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for systems wit
We formulate and prove a very general relative version of the Dobrushin-Lanford-Ruelle theorem which gives conditions on constraints of configuration spaces over a finite alphabet such that for every absolutely summable relative interaction, every tr
Standard derivations of the functional integral in non-equilibrium quantum field theory are based on the discrete time representation. In this work we derive the non-equilibrium functional integral for non-interacting bosons and fermions using a cont