Non-Markovian thermal operations boosting the performance of quantum heat engines

Quantum effects in ion transport: A thermodynamic resource theory approach

In recent years, understanding thermodynamics in the quantum regime has garnered significant attention, driven by advances in nanoscale physics and experimental techniques. In parallel, growing evidence supports the importance of quantum effects in various biological processes, making them increasingly relevant to quantum thermodynamics. In this study, we apply resource theory formulations of thermodynamics to investigate the role of quantum properties in ion transport across cell membranes. Within this framework, quantum properties are treated as resources under generalized thermodynamic constraints in the quantum regime. Specifically, our findings reveal that non-Markovianity, which reflects memory effects in ion transport dynamics, is a key quantum resource that enhances the yield and efficiency of the ion transport process. In contrast, quantum coherence, manifested as the superposition of energy states in ion-transport proteins, reduces these metrics but plays a crucial role in distinguishing between ion channels and ion pumps-two distinct types of ion-transport proteins in cell membranes. Finally, we demonstrate that introducing an additional coherent system allows coherence to facilitate the transformation of an ion pump into an ion channel.

Spectral density modulation and universal Markovian closure of fermionic environments

The combination of chain-mapping and tensor-network techniques provides a powerful tool for the numerically exact simulation of open quantum systems interacting with structured environments. However, these methods suffer from a quadratic scaling with the physical simulation time, and therefore, they become challenging in the presence of multiple environments. This is particularly true when fermionic environments, well-known to be highly correlated, are considered. In this work, we first illustrate how a thermo-chemical modulation of the spectral density allows replacing the original fermionic environments with equivalent, but simpler, ones. Moreover, we show how this procedure reduces the number of chains needed to model multiple environments. We then provide a derivation of the fermionic Markovian closure construction, consisting of a small collection of damped fermionic modes undergoing a Lindblad-type dynamics and mimicking a continuum of bath modes. We describe, in particular, how the use of the Markovian closure allows for a polynomial reduction of the time complexity of chain-mapping based algorithms when long-time dynamics are needed.

Catalytic enhancement in the performance of the microscopic two-stroke heat engine

We consider a model of heat engine operating in the microscopic regime: the two-stroke engine. It produces work and exchanges heat in two discrete strokes that are separated in time. The working body of the engine consists of two d-level systems initialized in thermal states at two distinct temperatures. Additionally, an auxiliary nonequilibrium system called catalyst may be incorporated with the working body of the engine, provided the state of the catalyst remains unchanged after the completion of a thermodynamic cycle. This ensures that the work produced by the engine arises solely from the temperature difference. Upon establishing the rigorous thermodynamic framework, we characterize twofold improvement stemming from the inclusion of a catalyst. Firstly, we prove that in the noncatalytic scenario, the optimal efficiency of the two-stroke heat engine with a working body composed of two-level systems is given by the Otto efficiency, which can be surpassed by incorporating a catalyst with the working body. Secondly, we show that incorporating a catalyst allows the engine to operate in frequency and temperature regimes that are not accessible for noncatalytic two-stroke engines. We conclude with a general conjecture about the advantage brought by a catalyst: including the catalyst with the working body always allows to improve efficiency over the noncatalytic scenario for any microscopic two-stroke heat engines. We prove this conjecture for two-stroke engines where the working body is composed of two d-level systems initialized in thermal states at two distinct temperatures, as long as the final joint state leading to optimal efficiency in the noncatalytic scenario is not a product state, or at least one of the d-level system is not thermal.

Quantum non-Markovianity, quantum coherence and extractable work in a general quantum process

A key concept in quantum thermodynamics is extractable work, which specifies the maximum amount of work that can be extracted from a quantum system. Different quantities are used to measure extractable work, the most prevalent of which are ergotropy and the difference between the non-equilibrium and equilibrium quantum free energies. Using the latter, we investigate the evolution of extractable work when an open quantum system undergoes a general quantum process described by a completely-positive and trace-preserving dynamical map. We derive a fundamental equation of thermodynamics for such processes as a relation between the distinct sorts of energy change in such a way that the first and the second law of thermodynamics are combined. We then identify the contributions from the reversible and irreversible processes in this equation and demonstrate that they are respectively responsible for the evolution of heat and extractable work of the open quantum system. Furthermore, we show how this correspondence between irreversibility and extractable work has the potential to provide a clear explanation of how the quantum properties of a system affect its extractable work evolution. Specifically, we establish this by directly connecting the change in extractable work with the change in standard quantifiers of quantum non-Markovianity and quantum coherence during a general quantum process. We illustrate these results with two examples.

Strongly coupled quantum Otto cycle with single qubit bath

We discuss a model of a closed quantum evolution of two qubits where the joint Hamiltonian is so chosen such that one of the qubits acts as a bath and thermalizes the other qubit which is acting as the system. The corresponding exact master equation for the system is derived. Interestingly, for a specific choice of parameters the master equation takes the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) form, with constant coefficients representing pumping and damping of a single qubit system. Based on this model we construct an Otto cycle connected to a single qubit bath and study its thermodynamic properties. Our analysis goes beyond the conventional weak coupling scenario and illustrates the effects of finite baths, including non-Markovianity. We find closed form expressions for efficiency (coefficient of performance), power (cooling power) for the heat engine regime (refrigerator regime), and for different modifications of the joint Hamiltonian.