Full counting statistics and coherences: fluctuation symmetry in heat
transport with the Unified quantum master equation
- URL: http://arxiv.org/abs/2212.11307v1
- Date: Wed, 21 Dec 2022 19:01:52 GMT
- Title: Full counting statistics and coherences: fluctuation symmetry in heat
transport with the Unified quantum master equation
- Authors: Matthew Gerry, Dvira Segal
- Abstract summary: We investigate statistics of energy currents through open quantum systems with nearly degenerate levels.
We find that maintaining coherences between nearly degenerate levels is essential for the properly capturing the current and its cumulants.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Recently, a "Unified" quantum master equation was derived and shown to be of
the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) form. This equation describes
the dynamics of open quantum systems in a manner that forgoes the full secular
approximation and retains the impact of coherences between eigenstates close in
energy. We implement full counting statistics with the Unified quantum master
equation to investigate the statistics of energy currents through open quantum
systems with nearly degenerate levels. We show that, in general, this equation
gives rise to dynamics that satisfy fluctuation symmetry, a sufficient
condition for the Second Law of Thermodynamics at the level of average fluxes.
For systems with nearly degenerate energy levels, such that coherences build
up, the Unified equation is simultaneously thermodynamically consistent and
more accurate than the fully Secular master equation. We exemplify our results
for a "V" system facilitating energy transport between two thermal baths at
different temperatures. We compare the statistics of steady-state heat currents
through this system as predicted by the Unified equation to those given by the
Redfield equation, which is less approximate but, in general, not
thermodynamically consistent. We also compare results to the Secular equation,
where coherences are entirely abandoned. We find that maintaining coherences
between nearly degenerate levels is essential for the properly capturing the
current and its cumulants. On the other hand, the relative fluctuations of the
heat current, which embody the thermodynamic uncertainty relation, display
inconsequential dependence on quantum coherences.
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