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Recent studies have revealed a deep connection between the asymmetry ofcross-correlations and thermodynamic quantities in the short-time limit. Inthis Letter, we address the finite-time domain of the asymmetry for both openclassical and quantum systems. Focusing on Markovian dynamics, we show that theasymmetry observed in finite-time cross-correlations is upper bounded bydissipation. We prove that, for classical systems in a steady state witharbitrary operational durations, the asymmetry exhibits, at most, linear growthover time, with the growth speed determined by the rates of entropy productionand dynamical activity. In the long-time regime, the asymmetry exhibitsexponential decay, with the decay rate determined by the spectral gap of thetransition matrix. Remarkably, for quantum cases, quantum coherence is equallyimportant as dissipation in constraining the asymmetry of correlations. Wedemonstrate an example where only quantum coherence bounds the asymmetry whilethe entropy production rate vanishes. Furthermore, we generalize the short-timebounds on correlation asymmetry, as reported by Shiraishi [arXiv:2304.12775]and Ohga et al. [arXiv:2303.13116], to encompass finite-time scenarios. Thesefindings offer novel insights into the thermodynamic aspects of correlationasymmetry.

Dissipation, quantum coherence, and asymmetry of finite-time cross-correlations