Nonlinear Energy Response in Free Energy Landscape Picture

A theory for the nonlinear energy response of a system subjected to a heat bath is developed for the case in which the temperature of the heat bath is modulated sinusoidally. The theory is applied to a nonequilibrium system described by the free energy landscape picture. The following are shown (1) The ac specific heat is represented by the superposition of the Debye relaxations with different relaxation times, which correspond to eigenvalues of the transition rate matrix for the jump motion among basins in the landscape. (2) The 2nd-order energy response consists of two terms; oscillating and nonoscillating terms. The 2nd-order ac specific heat is defined for the first time from the oscillating term. (3) In the high-frequency limit, the 2nd-order ac specific heat and the nonoscillating term of the 2nd-order energy response are proportional to the 2nd temperature derivative of the transition rate. To show the validity of the formalism, a two-basin system is analyzed, where the barrier between two basins d...