Geometric fluctuation theorem for a spin-boson system

Abstract

We derive an extended fluctuation theorem for geometric pumping of a spin-boson system under periodic control of environmental temperatures by using a Markovian quantum master equation. We obtain the current distribution, the average current, and the fluctuation in terms of the Monte Carlo simulation. To explain the results of our simulation we derive an extended fluctuation theorem. This fluctuation theorem leads to the fluctuation dissipation relations but the absence of the conventional reciprocal relation.

Geometric phaselike effects in a quantum heat engine

“…Random fluctuations affect the transport properties and are usually studied via a full counting statistics (FCS) [30,31] method that involves calculation of moments and cumulants of P (q, t), the probability distribution function (PDF) for the number (q) of particles exchanged between system and reservoir in a measurement time t. FCS led to the steady state fluctuation theorems (FT) [25,[32][33][34][35][36], the cornerstones of quantum thermodynamics [37]. Recently, it was reported that during transport across quantum junctions [7,38], the standard mathematical form of the FT is broken due to the emergence of PBp and hence attempts have been made to establish geometric FTs [39] in spin-boson systems. We observe the same violation of the FT in our QHE.…”

Pumping current in a non-Markovian $N$-state model

“…non-adiabatic effects, have also been investigated for this model [20]. Furthermore, it has been shown that the presence of the BSN phase engenders non-gaussianity of the system fluctuations, leading to a modified form of the fluctuation theorem for geometrical pumping [21,22].…”

Nonequilibrium fluctuations of a driven quantum heat engine via machine learning

“…This problem is further aggravated when a few parameters of the system are modulated in time. It has been recently shown in both electron and heat transport that externally driving the * hpgoswami@pks.mpg.de temperature of reservoirs results in geometric augmentations (Pancharatnam-Berry phaselike (PBp) effects) to the cumulants when evaluated via the master equation method [21][22][23][24]. Such geometric contributions or PBp effects have strange ramifications on the overall statistics, for example, violation of the standard mathematical nonequilibrium fluctuation relations [21,[24][25][26].…”