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We consider the stationary states of a chain of $n$ anharmonic coupledoscillators, whose deterministic hamiltonian dynamics is perturbed by randomindependent sign change of the velocities (a random mechanism that conserveenergy). The extremities are coupled to thermostats at different temperature$T_\ell$ and $T_r$ and subject to constant forces $\tau_\ell$ and $\tau_r$. Ifthe forces differ $\tau_\ell \neq \tau_r$ the center of mass of the system willmove of a speed $V_s$ inducing a tension gradient inside the system. Our aim isto see the influence of the tension gradient on the thermal conductivity. Weinvestigate the entropy production properties of the stationary states, and weprove the existence of the Onsager matrix defined by Green-kubo formulas(linear response). We also prove some explicit bounds on the thermalconductivity, depending on the temperature.

Transport Properties of a Chain of Anharmonic Oscillators with random flip of velocities