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In this work, we establish an exact relation which connects the heat exchange between two systems initialized in their thermodynamic equilibrium states at different temperatures and the R\'{e}nyi divergences between the initial thermodynamic equilibrium state and the final non-equilibrium state of the total system. The relation tells us that the various moments of the heat statistics are determined by the Renyi divergences between the initial equilibrium state and the final non-equilibrium state of the global system. In particular the average heat exchange is quantified by the relative entropy between the initial equilibrium state and the final non-equilibrium state of the global system. The relation is applicable to both finite classical systems and finite quantum systems., Comment: 5 pages

In this work, we show that a universal quantum work relation for a quantum system driven arbitrarily far from equilibrium extends to a parity-time- (PT-) symmetric quantum system with unbroken PT symmetry, which is a consequence of microscopic reversibility. The quantum Jarzynski equality, linear response theory, and Onsager reciprocal relations for the PT-symmetric quantum system are recovered as special cases of the universal quantum work relation in a PT-symmetric quantum system. In the regime of broken PT symmetry, the universal quantum work relation does not hold because the norm is not preserved during the dynamics.