Equivalence of thermostatted nonlinear responses

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Abstract
In this paper we show that, in general, both steady-state averages and time correlation functions computed under Gaussian isokinetic dynamics, Gaussian isoenergetic dynamics, or Nosé-Hoover thermostats are all equal. This result is true even in the far-from-equilibrium nonlinear regime as long as the system is mixing and the quantities involved are local and not trivially related to constants of the motion. We provide computer-simulation results that support this theoretical prediction.