Response of a thermodynamic system to a slowly varying mechanical perturbation

A study is made of the change of the statistical mean values of a system in a slowly varying external field. Under the assumption of a large specific heat, an expansion is obtained in powers of the rate of change of the field to terms of second order. The linear term of the expansion differs from the corresponding expression of linear response theory only by the fact that it contains the adiabatic time correlation function, in which the evolution is determined by the instantaneous Hamiltonian without allowance for its time dependence and the averaging is made with the instantaneously equilibrium statistical operator. As an illustration, a study is made of the change of the mean position of a one-dimensional anharmonie Brownian oscillator after the force that acts on it has ceased (creep).