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Nonadiabatic evolution and thermodynamics for a boundary-driven system with a weak intrasubsystem interaction (2404.14081v2)

Published 22 Apr 2024 in quant-ph

Abstract: We derive a time-dependent master equation for an externally driven system whose subsystems weakly interact with each other and locally connect to the thermal reservoirs. The nonadiabatic equation obtained here can be viewed as a generalization of the local master equation, which has already been extensively used in describing the dynamics of a boundary-driven system. In addition, we investigate the fundamental reason underlying the thermodynamic inconsistency generated by the local and nonadiabatic master equations. We fnd that these two equations are consistent with the second law of thermodynamics when the system is far away from the steady state, while they give rise to the contradiction at the steady state. Finally, we numerically confrm our results by considering a toy model consisting of two qubits and two local heat baths.

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  38. The phase factor ϕn⁢(t)subscriptitalic-ϕ𝑛𝑡\phi_{n}(t)italic_ϕ start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT ( italic_t ) is non-degenerate means that we have n=m𝑛𝑚n=mitalic_n = italic_m when ϕn⁢m⁢(t)=0subscriptitalic-ϕ𝑛𝑚𝑡0\phi_{nm}(t)=0italic_ϕ start_POSTSUBSCRIPT italic_n italic_m end_POSTSUBSCRIPT ( italic_t ) = 0, while ϕn⁢m⁢(t)subscriptitalic-ϕ𝑛𝑚𝑡\phi_{nm}(t)italic_ϕ start_POSTSUBSCRIPT italic_n italic_m end_POSTSUBSCRIPT ( italic_t ) is non-degenerate implies that we have n=n′𝑛superscript𝑛′n=n^{\prime}italic_n = italic_n start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT and m=m′𝑚superscript𝑚′m=m^{\prime}italic_m = italic_m start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT under the conditions of ϕn⁢m⁢(t)≠0subscriptitalic-ϕ𝑛𝑚𝑡0\phi_{nm}(t)\neq 0italic_ϕ start_POSTSUBSCRIPT italic_n italic_m end_POSTSUBSCRIPT ( italic_t ) ≠ 0 and ϕn⁢m⁢(t)=ϕn′⁢m′⁢(t)subscriptitalic-ϕ𝑛𝑚𝑡subscriptitalic-ϕsuperscript𝑛′superscript𝑚′𝑡\phi_{nm}(t)=\phi_{n^{\prime}m^{\prime}}(t)italic_ϕ start_POSTSUBSCRIPT italic_n italic_m end_POSTSUBSCRIPT ( italic_t ) = italic_ϕ start_POSTSUBSCRIPT italic_n start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT italic_m start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT end_POSTSUBSCRIPT ( italic_t ). See the toy model discussed in Sec. V as an example.
  39. Without loss of the generality, here we assume fi⁢(0)=0subscript𝑓𝑖00f_{i}(0)=0italic_f start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ( 0 ) = 0.

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