We study quantum thermodynamics in nonequilibrium reservoirs (NERs) that are prepared from initially thermal ones via unitary driving processes. Based on the formulation of entropy production in NERs, we establish a Landauer-like bound and show that the bound can be violated under a definite condition depending on the states of NERs. It is found that the breakdown of this Landauer-like bound implies occurrences of several anomalous phenomena in NERs, namely, the efficiency enhancement of quantum thermal machines beyond the Carnot limit, the extraction of work from a single reservoir, and the spontaneous heat flow from a cold reservoir to a hot one. The results are illustrated through a physical model taking the preparation processes of NERs into account. Our work sheds light on the reason and condition of some unusual phenomena occurring in NERs and is helpful for one to prepare effective NERs that can be used as quantum resources to realize certain thermodynamic tasks.
We study quantum thermodynamics in nonequilibrium reservoirs (NERs) that are prepared from initially thermal ones via unitary driving processes. Based on the formulation of entropy production in NERs, we establish a Landauer-like bound and show that the bound can be violated under a definite condition depending on the states of NERs. It is found that the breakdown of this Landauer-like bound implies occurrences of several anomalous phenomena in NERs, namely, the efficiency enhancement of quantum thermal machines beyond the Carnot limit, the extraction of work from a single reservoir, and the spontaneous heat flow from a cold reservoir to a hot one. The results are illustrated through a physical model taking the preparation processes of NERs into account. Our work sheds light on the reason and condition of some unusual phenomena occurring in NERs and is helpful for one to prepare effective NERs that can be used as quantum resources to realize certain thermodynamic tasks.
Landauer's principle, a cornerstone of quantum information and thermodynamics, appears to be violated when the thermal reservoir is replaced by a squeezed thermal state (STS), owing to the additional thermodynamic resources inherently present in the squeezed state. We introduce a formal extension of the principle to such unitarily transformed thermal states. By defining an effective Hamiltonian, we rigorously establish a generalized Landauer inequality, which naturally reduces to the standard case for an ordinary thermal reservoir as a special instance. The framework further yields a consistent definition of entropy production and a proof of its non-negativity. We illustrate its utility by studying an arbitrarily moving Unruh-DeWitt detector coupled to a quantum field initially prepared in the STS. Using perturbation theory, we compute the entropy production explicitly, confirming its positivity. As a result of the symmetry breaking induced by the unitary transformation, it depends on both the proper time interval and the absolute spacetime position. Our work resolves the apparent violation of Landauer's principle with STSs. It also provides a robust tool for analyzing quantum thermodynamics in non-equilibrium and relativistic settings, with potential implications for quantum thermal machines and information protocols.
Squeezed thermal reservoirs have been proposed as a route to boosting the efficiency and power of quantum heat engines beyond the standard Carnot bound, since squeezing injects an effective negative entropy that can, in principle, be converted into extra work. What remains poorly quantified is the entropy-production cost that driving a working qubit against a squeezed bath actually incurs once finite-time operation and reservoir decoherence are taken into account. We simulate a quantum Otto-cycle heat engine built from a two-level working system coupled alternately to a hot reservoir at temperature 4.2 K, squeezed with squeezing parameter r ranging from 0 to 1.2, and an unsqueezed cold reservoir at 0.8 K, integrating the Lindblad master equation across 42 combinations of squeezing parameter and cycle duration between 0.05 and 2.0 (in units of the inverse qubit gap). At r = 0, mean entropy production per cycle was 0.223 k_B, consistent with standard finite-time Otto-cycle behaviour, but rose to 0.361 k_B at r = 1.2, a 62% increase, even as extractable work per cycle increased by 41%, from 0.184 to 0.259 (in units of the qubit gap). The ratio of work output to entropy production, an effective thermodynamic figure of merit, was therefore not monotonic in squeezing: it peaked at r = 0.6, where work per unit entropy produced reached 0.98, 15% above the unsqueezed value of 0.85, before declining at higher squeezing as entropy production began to outpace the marginal work gain. Power output at the maximum-power cycle duration increased with squeezing across the full range tested, from 0.31 (gap units) at r = 0 to 0.52 at r = 1.2, a 68% gain, but efficiency at maximum power fell from 0.41 to 0.33 over the same range, a trade-off traced out in detail in Table 1. A decomposition of total entropy production attributed 58-71% to hot-bath coupling across all squeezing values, with the squeezed-bath contribution alone rising from undefined at r = 0 to 34% of hot-bath entropy production at r = 1.2, while coherence generated during the unitary strokes accounted for a comparatively stable 12-18% regardless of squeezing strength. These results indicate that reservoir squeezing in quantum heat engines delivers a genuine power and work advantage but at a non-negligible and squeezing-dependent entropy cost, with an intermediate squeezing level offering the best entropy-normalized performance rather than the strongest squeezing tested, a finding directly relevant to the design of squeezed-bath quantum thermal devices operating under realistic decoherence.
A statistical mechanical formulation where nonequilibrium averages of selected quantum observables are given exactly as averages over local density operators is used to describe the dynamics and thermodynamics of a small quantum system coupled to reservoirs. The local density operators are functionals of constraint variables that play the role of thermodynamic forces that satisfy a set of equations of motion. A focus of the work is on the evolution of the average internal energy of the quantum subsystem that may be subject to external autonomous driving that does work on the system, and on entropy production in the system. The nonequilibrium statistical thermodynamics the quantum subsystem coupled to reservoirs, as well as that for the isolated subsystem and reservoirs, are discussed. When the subsystem is coupled to large quantum reservoirs, the effects of the quantum subsystem on the reservoirs can be captured through boundary conditions on the reservoir equations, and these boundary conditions are derived. The formulation is illustrated by considering the heat transfer through a system comprising a quantum system coupled to two heat reservoirs with different temperatures.
We assess two different nonequilibrium quantum Landauer bounds: the traditional approach based on the change in entropy, referred to as the ``entropic bound,'' and one based on the details of the dynamical map, referred to as the ``thermodynamic bound.'' By first restricting to a simple exactly solvable model of a single two-level system coupled to a finite-dimensional thermal environment and by exploiting an excitation-preserving interaction, we establish the dominant role played by the population terms in dictating the tightness of these bounds with respect to the dissipated heat and clearly establish that coherences only affect the entropic bound. Furthermore, we show that sharp boundaries between the relative performance of the two quantities emerge and find that there are clear instances where both approaches return a bound weaker than Clausius' statement of the second law, rendering them ineffective. Finally, we show that our results extend to generic interaction terms.
We study the validity of the Landauer principle in the non-Markovian regime by means of collisional models where the intracollisions inside the reservoir cause memory effects generating system-environment correlations. We adopt the system-environment correlations created during the dynamical process to assess the effect of non-Markovianity on the Landauer principle. Exploiting an exact equality for the entropy change of the system, we find the condition for the violation of the Landauer principle, which occurs when the established system-environment correlations become larger than a threshold. We then generalize the study to the nonequilibrium situation where the system is surrounded by many reservoirs at different temperatures. Our results, verified through collisional models with Heisenberg-type interactions, suggest that the complexity of the environment does not play a significant role in the qualitative mechanisms underlying the violation of the Landauer principle under non-Markovian processes.
We expand the standard thermodynamic framework of a system coupled to a thermal reservoir by considering a stream of independently prepared units repeatedly put into contact with the system. These units can be in any nonequilibrium state and interact with the system with an arbitrary strength and duration. We show that this stream constitutes an effective resource of nonequilibrium free energy and identify the conditions under which it behaves as a heat, work or information reservoir. We also show that this setup provides a natural framework to analyze information erasure ("Landauer's principle") and feedback controlled systems ("Maxwell's demon"). In the limit of a short system-unit interaction time, we further demonstrate that this setup can be used to provide a thermodynamically sound interpretation to many effective master equations. We discuss how non-autonomously driven systems, micromasers, lasing without inversion, and the electronic Maxwell demon, can be thermodynamically analyzed within our framework. While the present framework accounts for quantum features (e.g. squeezing, entanglement, coherence), we also show that quantum resources do not offer any advantage compared to classical ones in terms of the maximum extractable work.