Heat Flow in a Periodically Forced, Thermostatted Chain II

Abstract We derive a macroscopic heat equation for the temperature of pinned harmonic chain subject to periodic force at its right side and in contact with bath left side. The microscopic dynamics bulk is given by Hamiltonian motion plus reversal velocity particle occurring independently each exponential times, rate $$\gamma $$ γ . latter produces finite conductivity. Starting an initial probability distribution n particles we compute current local expected value energy. Scaling space time diffusively yields, $$n\rightarrow +\infty n → + ∞ limit, profile T ( t , u ), $$t>0$$ t > 0 $$u \in [0,1]$$ u ∈ [ , 1 ] It be solved conditions (0, ) specified $$T(t,0)=T_-$$ T ( ) = - reservoir fixed flux J entering system $$u=1$$ | equals work done which computed explicitly