According to the second law, the efficiency of cyclic heat engines is limited by the Carnot bound that is attained by engines that operate between two thermal baths under the reversibility condition whereby the total entropy does not increase. Quantum engines operating between a thermal and a squeezed-thermal bath have been shown to surpass this bound. Yet, their maximum efficiency cannot be determined by the reversibility condition, which may yield an unachievable efficiency bound above unity. Here we identify the fraction of the exchanged energy between a quantum system and a bath that necessarily causes an entropy change and derive an inequality for this change. This inequality reveals an efficiency bound for quantum engines energised by a non-thermal bath. This bound does not imply reversibility, unless the two baths are thermal. It cannot be solely deduced from the laws of thermodynamics.

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We consider a two-level quantum system prepared in an arbitrary initial state and relaxing to a steady state due to the action of a Markovian dissipative channel. We study how optimal control can be used for speeding up or slowing down the relaxation towards the fixed point of the dynamics. We analytically derive the optimal relaxation times for different quantum channels in the ideal ansatz of unconstrained quantum control (a magnetic field of infinite strength). We also analyze the situation in which the control Hamiltonian is bounded by a finite threshold. As byproducts of our analysis we find that: (i) if the qubit is initially in a thermal state hotter than the environmental bath, quantum control cannot speed up its natural cooling rate; (ii) if the qubit is initially in a thermal state colder than the bath, it can reach the fixed point of the dynamics in finite time if a strong control field is applied; (iii) in the presence of unconstrained quantum control it is possible to keep the evolved state indefinitely and arbitrarily close to special initial states which are far away from the fixed points of the dynamics.

We study the generation of defects when a quantum spin system is quenched through a multicritical point by changing a parameter of the Hamiltonian as t/τ , where τ is the characteristic time scale of quenching. We argue that when a quantum system is quenched across a multicritical point, the density of defects (n) in the final state is not necessarily given by the Kibble-Zurek scaling form n ∼ 1/τ dν/(zν+1) , where d is the spatial dimension, and ν and z are respectively the correlation length and dynamical exponent associated with the quantum critical point. We propose a generalized scaling form of the defect density given by n ∼ 1/τ d/(2z 2 ) , where the exponent z2 determines the behavior of the off-diagonal term of the 2 × 2 Landau-Zener matrix at the multicritical point. This scaling is valid not only at a multicritical point but also at an ordinary critical point.

We study scaling behavior of the geometric tensor χ α,β (λ1, λ2) and the fidelity susceptibility (χF) in the vicinity of a quantum multicritical point (MCP) using the example of a transverse XY model. We show that the behavior of the geometric tensor (and thus of χF) is drastically different from that seen near a critical point. In particular, we find that is highly non-monotonic function of λ along the generic direction λ1 ∼ λ2 = λ when the system size L is bounded between the shorter and longer correlation lengths characterizing the MCP: 1/|λ| ν 1 ≪ L ≪ 1/|λ| ν 2 , where ν1 < ν2 are the two correlation length exponents characterizing the system. We find that the scaling of the maxima of the components of χ αβ is associated with emergence of quasi-critical points at λ ∼ 1/L 1/ν 1 , related to the proximity to the critical line of finite momentum anisotropic transition. This scaling is different from that in the thermodynamic limit L ≫ 1/|λ| ν 2 , which is determined by the conventional critical exponents. We use our results to calculate the defect density following a rapid quench starting from the MCP and show that it exerts a step-like behavior for small quench amplitudes. Study of heat density and diagonal entropy density also show signatures of quasi-critical points.

We study the quenching dynamics of a one-dimensional spin-1/2 XY model in a transverse field when the transverse field h(= t/τ ) is quenched repeatedly between −∞ and +∞. A single passage from h → −∞ to h → +∞ or the other way around is referred to as a half-period of quenching. For an even number of half-periods, the transverse field is brought back to the initial value of −∞; in the case of an odd number of half-periods, the dynamics is stopped at h → +∞. The density of defects produced due to the non-adiabatic transitions is calculated by mapping the many-particle system to an equivalent Landau-Zener problem and is generally found to vary as 1/ √ τ for large τ ;however, the magnitude is found to depend on the number of half-periods of quenching. For two successive half-periods, the defect density is found to decrease in comparison to a single half-period, suggesting the existence of a corrective mechanism in the reverse path. A similar behavior of the density of defects and the local entropy is observed for repeated quenching. The defect density decays as 1/ √ τ for large τ for any number of half-periods, and shows a increase in kink density for small τ for an even number; the entropy shows qualitatively the same behavior for any number of half-periods. The probability of non-adiabatic transitions and the local entropy saturate to 1/2 and ln 2, respectively, for a large number of repeated quenching.

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We study optimal control strategies to optimize the relaxation rate towards the fixed point of a quantum system in the presence of a non-Markovian (NM) dissipative bath. Contrary to naive expectations that suggest that memory effects might be exploited to improve optimal control effectiveness, NM effects influence the optimal strategy in a non trivial way: we present a necessary condition to be satisfied so that the effectiveness of optimal control is enhanced by NM subject to suitable unitary controls. For illustration, we specialize our findings for the case of the dynamics of single qubit amplitude damping channels. The optimal control strategy presented here can be used to implement optimal cooling processes in quantum technologies and may have implications in quantum thermodynamics when assessing the efficiency of thermal micro-machines.