The Second Law of Thermodynamics defines the "arrow of time, " characterizing the irreversibility of macroscopic processes. However, providing a rigorous proof of the Second Law is notoriously difficult.
One of the challenges is Loschmidt's paradox, which questions how time-symmetric fundamental dynamics can give rise to a distinction between past and future. We propose a formulation of the Second Law that reconciles the reversibility of microscopic dynamics with macroscopic irreversibility. This formulation enables a rigorous proof that applies to both classical and quantum closed systems. [arXiv:1801.08768]
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