Shi Z, Abe S. Quantum Weak Invariants: Dynamical Evolution of Fluctuations and Correlations.
Entropy (Basel) 2020;
22:e22111219. [PMID:
33286987 PMCID:
PMC7711532 DOI:
10.3390/e22111219]
[Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 09/08/2020] [Revised: 10/15/2020] [Accepted: 10/21/2020] [Indexed: 11/16/2022]
Abstract
Weak invariants are time-dependent observables with conserved expectation values. Their fluctuations, however, do not remain constant in time. On the assumption that time evolution of the state of an open quantum system is given in terms of a completely positive map, the fluctuations monotonically grow even if the map is not unital, in contrast to the fact that monotonic increases of both the von Neumann entropy and Rényi entropy require the map to be unital. In this way, the weak invariants describe temporal asymmetry in a manner different from the entropies. A formula is presented for time evolution of the covariance matrix associated with the weak invariants in cases where the system density matrix obeys the Gorini-Kossakowski-Lindblad-Sudarshan equation.
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