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 super-position 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 diverges at a certain temperature To. The 2nd-order ac specific heat has extrema as a function of the frequency, which diverges at To. A similar behavior appears in the high-frequency limit of the nonoscillating term of the 2nd-order energy response.