Paper detail

Non-Markovian and Thermodynamic Signatures in the Classicality Assessment via Kolmogorov Consistency

The Kolmogorov consistency condition (KCC) defines the statistical boundary between classical and quantum dynamics. Its violation signifies the breakdown of a classical Markov description of temporal correlations. In this work, we establish a direct analytical connection between KCC violation and non-Markovianity in open quantum dynamics, revealing how memory effects manifest as departures from classical probabilistic consistency. Within a generic two-level open quantum system framework, we establish quantitative connections between the magnitude of KCC violation and key information-theoretic and thermodynamic quantities, such as mutual information, the Fano factor, heat exchange, and entropy production rate, thereby enabling a thermodynamic interpretation of temporal quantum correlations. Furthermore, we uncover formal correspondences between KCC violation, the Leggett-Garg inequality, and the negativity of the Kirkwood-Dirac quasi-distribution, identifying them as complementary witnesses of temporal quantum non-classicality. Our results thus provide a unified framework linking information-theoretic, thermodynamic, and temporal indicators of quantumness in open quantum systems.