Temperature correction to dichotomic fluctuation models for open quantum system dynamics

We investigate the dynamics of an asymmetric two-level system (TLS) subject to stochastic energy fluctuations described by a dichotomic Markov process, which is a powerful model applicable to excitonic transport in molecular aggregates, decoherence in qubits, and spectral fluctuations in single-molecule spectroscopy. While the standard dichotomic noise model offers exact solutions that capture non-Markovian dynamics, it violates detailed balance and fails to ensure thermal equilibrium. To overcome this, we introduce a temperature-corrected version by adding a counterterm to the exact equations of motion, thereby restoring the correct equilibrium behavior. Furthermore, we explore the TLS dynamics under varying initial conditions and parameter regimes. The results demonstrate that the model reproduces both short-time coherent evolution and long-time thermal populations and captures single-system behavior relevant to experiments on isolated quantum systems. This work provides a powerful framework for studying non-Markovian dynamics in open quantum systems.