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Apparent temperature: demystifying the relation between quantum coherence, correlations, and heat flows

Heat exchanges are the essence of Thermodynamics. In order to investigate non-equilibrium effects like quantum coherence and correlations in heat flows we introduce the concept of apparent temperature. Its definition is based on the expression of the heat flow between out-of-equilibrium quantum systems. Such apparent temperatures contain crucial information on the role and impact of correlations and coherence in heat exchanges. In particular, both behave as populations, affecting dramatically the population balance and therefore the apparent temperatures and the heat flows. We show how seminal results can be re-obtained, offering an interesting alternative point of view. We also present new predictions and suggest a simple experiment to test them. Our results show how quantum and non-equilibrium effects can be used advantageously, finding applications in quantum thermal machine designs and non-equilibrium thermodynamics but also in collective-effect phenomena.