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Work relation in non-equilibrium steady states of one-dimensional quantum lattice systems. (English) Zbl 1458.82015

Summary: We consider the non-equilibrium steady state induced by two infinitely extended quantum thermal reservoirs at different inverse temperatures \(\beta + \Delta \beta, \beta - \Delta \beta\) and derive a work relation. We consider global cyclic operations and derive an upper bound of the work density in one-dimensional quantum lattice systems. This relation reproduces the second law of thermodynamics in the equilibrium limit \(\Delta \beta \rightarrow 0\). A free fermion system is discussed as an example, and the physical interpretation is given to the upper bound.
©2021 American Institute of Physics

MSC:

82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
80A10 Classical and relativistic thermodynamics
82C35 Irreversible thermodynamics, including Onsager-Machlup theory
82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
82B30 Statistical thermodynamics
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