Nonequilibrium thermodynamic entropy during waiting-time evolution

Determine how the nonequilibrium thermodynamic entropy evolves during the waiting time in the return-quench protocol, including whether it approaches its asymptotic value monotonically or can overshoot before relaxing, by analyzing the subsystem entropy analytically or numerically.

Background

The paper studies a return-quench protocol in the large-N, large-q Sachdev–Ye–Kitaev model. Although post-quench correlators within a single time interval coincide with those of a thermal reference state, mixed-time correlators retain nonequilibrium memory that decays during the waiting interval. The parameter theta is associated with the coarse-grained entropy of the corresponding thermal reference state, but this association is established only asymptotically after the mixed-time memory has decayed.

The unresolved issue concerns the entropy at finite waiting time. From a subsystem perspective, theta can be related to entanglement entropy, and the paper notes that this quantity need not approach its asymptotic value monotonically. The authors specifically identify the possibility of an overshoot followed by relaxation and propose studying subsystem entropy analytically or numerically to resolve its behavior.