Time-Energy Uncertainty and short-time Nonequilirium Thermodynamics


Erez, N. (2008). Time-Energy Uncertainty and short-time Nonequilirium Thermodynamics. Perimeter Institute. https://pirsa.org/08090083


Erez, Noam. Time-Energy Uncertainty and short-time Nonequilirium Thermodynamics. Perimeter Institute, Sep. 30, 2008, https://pirsa.org/08090083


          @misc{ pirsa_08090083,
            doi = {10.48660/08090083},
            url = {https://pirsa.org/08090083},
            author = {Erez, Noam},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Time-Energy Uncertainty and short-time Nonequilirium Thermodynamics},
            publisher = {Perimeter Institute},
            year = {2008},
            month = {sep},
            note = {PIRSA:08090083 see, \url{https://pirsa.org}}

Noam Erez Weizmann Institute of Science


As is well known, time-energy uncertainty generically manifests itself in the short time behavior of a system weakly coupled to a bath, in the energy non-conservation of the interaction term (H_I does not commute with H_0). Similarly, the monotonic evolution of the system density operator to its equilibrium value which is a universal property of quantum dynamical semigroups (Spohn\'s theorem), e.g., systems with Lindbladian evolution, is in general violated at short (non-Markovian) timescales. For example, frequent, brief non-demolition measurements of the energy states of a two level system (TLS) coupled to a bath, disturbs the thermal equilibrium between them, despite leaving the system and bath states separately unperturbed. For sufficiently short intervals between measurements (Zeno regime) the system and bath heat up immediately following the measurement. It is also possible to have net cooling in an intermediate (anti-Zeno-like) regime. The evolution of the system state away from its equilibrium value, not only violates the Markovian-dynamics version of the 2nd law (Spohn\'s theorem), but also Lindblad\'s theorem on which it rests, which is valid for any evolution described by a completely positive map. This does not imply that the evolution is not completely-positive, but rather that it is not a well-defined map at allthe evolution of the state of the system is not determined by this state alone (nor even together with the reduced state of the bath), but rather by the full joint system-bath state (this indeterminacy was shown previously, by Buzek et al., for special cleverly constructed joint states). Ref: N. Erez, G. Gordon, M. Nest & G. Kurizki, Nature 452, 724 (2008)