Majorization requires infinitely many second laws
Authors:
- Pedro HackPHPedro Hack
- Daniel A. BraunDBDaniel A. Braun
- Sebastian GottwaldSGSebastian Gottwald
Preprint
Abstract
Majorization is a fundamental model of uncertainty that possesses several applications in areas like thermodynamics or entanglement theory, and constitutes one of the pillars of the modern resource-theoretic approach to physics. Here, we improve on its relation to measurement apparatus. In particular, after discussing what the proper notion of second law in this scenario is, we show that, for a sufficiently large state space, any family of entropy-like functions constituting a second law is necessarily countably infinite. Moreover, we provide an analogous result for a variation of majorization known as thermo-majorization which, in fact, does not require any constraint on the state space provided the equilibrium distribution is not uniform. Lastly, we conclude by discussing the applicability of our results to molecular diffusion.Keywords
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