![]() ![]() The associated dotted line emphasises the asymptotic value of each curve, equal to n, the number of spins in the ensemble. The graph represents the plot of the ratio Π th / Π col as a function of ℏ ω β B for ℏ ω | β 0 | ≫ 1 and for ensembles containing n = 2 (orange curve), n = 4 (red curve), and n = 10 (purple curve) spins s = 1 / 2. The associated entropy production is denoted by Π col. The ensemble reaches the equilibrium state ρ β 0 ∞ ( β B ) (see Appendix pp5 for the detailed expression). The dissipation process with generation of horizontal coherences corresponds to collective dissipation of the spins. The associated entropy production is denoted by Π th. The ensemble reaches the thermal equilibrium state ρ th ( β B ). The dissipation process with no generation of horizontal coherences corresponds to independent dissipation of each spin. Ratio of the entropy production with and without generation of horizontal coherences. Some consequences for thermal machines and resource theory of coherence are suggested. Conservation laws of the different types of coherences are derived. Going further, we establish a complementarity relation between horizontal coherences and population convergence, which is particularly enlightening for understanding heat flow reversals. This includes phenomena such as generation of coherences between degenerate energy levels (called horizontal coherences), alteration of energy exchanges, and, last but not least, reversal of the natural convergence of the populations toward the thermal equilibrium state. Furthermore, such negative contributions are related to significant changes in the ongoing thermodynamics. Here we show that for degenerate (or near-degenerate) quantum systems there are additional quantum contributions which, remarkably, can become negative. For dissipation of quantum systems, it was recently shown that the entropy production contains indeed two contributions: a classical one and a quantum one. The entropy production in dissipative processes is the essence of the arrow of time and the second law of thermodynamics. ![]()
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