Lindbladian Thermal Machines Enhance Performance, Surpassing Landauer Limit with Geometric Heat Pumping

The pursuit of efficient thermal machines at the quantum scale faces fundamental challenges from energy dissipation and the limitations of small systems, but new research offers a pathway to enhance performance through careful control of entanglement. Gerónimo J. Caselli, Luis O. Manuel, and Liliana Arrachea, working at institutions including the Universidad Nacional de Rosario and the Centro Atómico Bariloche, present a detailed theoretical analysis of multi-qubit thermal machines using a Lindbladian approach. Their work systematically examines how energy flows within these devices, separating the effects of geometric and dissipative factors, and reveals that interactions between qubits can overcome established limits on heat pumping efficiency. This achievement establishes a general framework for optimising quantum heat engines and exploring the interplay between dissipation and performance in driven quantum systems.

Researchers at EA and Instituto Balseiro, Argentina, present a detailed analysis of slowly driven quantum thermal machines based on interacting qubits, utilising the Lindblad master equation. The team implements a systematic expansion in the driving rate, deriving explicit expressions for the rate of work exerted by the driving forces, the heat currents exchanged with the reservoirs, and the entropy production up to second order. This approach ensures full thermodynamic consistency within the linear-response regime, allowing for precise calculations of energy transfer and efficiency. The formalism naturally separates geometric and dissipative contributions, identified by a Berry curvature, providing a clearer understanding of the underlying mechanisms governing these quantum machines.

Quantum Thermodynamics and Finite-Time Processes

This research focuses on quantum thermodynamics, specifically exploring how geometric concepts and adiabatic processes can optimise nanoscale thermal machines and define the fundamental limits of quantum energy conversion. A key aim is to understand how to extract work and control heat flow in quantum systems, particularly in situations involving finite time and nonequilibrium processes. The work progresses towards designing and analysing quantum devices that achieve enhanced efficiency and performance through geometric principles. The research investigates several interconnected areas, including quantum heat engines, finite-time thermodynamics, nonequilibrium thermodynamics, and geometric thermodynamics.

A significant theme is the exploration of adiabatic processes, used to control energy flow and extract work, utilising the geometric Berry phase to enhance thermodynamic performance and investigating superabsorption to improve heat engine performance. The research also examines geometric optimisation and geometric quantities, applying concepts from the Cheeger problem to understand energy transport limits. Further investigations encompass quantum transport and open quantum systems, analysing how energy and information move within quantum systems and how they interact with their environment. Techniques like nonequilibrium Green’s functions and quantum master equations are employed to model these systems. The research also explores quantum pumping, using quantum effects to control electron transport in single-electron pumps, and examines fundamental limits and dissipation, including Landauer’s principle and the relationship between dissipation and noise immunity.

Geometric Heat and Landauer-Like Limits

Scientists have achieved a detailed understanding of thermal machines driven by interacting qubits, developing a theoretical framework based on the Lindblad master equation to analyse their performance. The work establishes explicit expressions for the rate of work, heat currents, and entropy production, accurate to second order in the driving rate, ensuring thermodynamic consistency within the linear-response regime. This formalism elegantly separates geometric and dissipative contributions, identifying a Berry curvature and a metric in parameter space that govern the machine’s behaviour. Analytical results demonstrate that the geometric heat pumped per cycle is bounded by a value analogous to the Landauer limit for entropy change.

Importantly, the team discovered that this bound can be surpassed when qubit interactions and asymmetric couplings to thermal reservoirs are introduced, opening possibilities for enhanced heat pumping efficiency. Numerical simulations of a two-qubit system reveal a significant role for qubit interactions and system-bath couplings in determining the dissipated power, highlighting the complex interplay between these factors. The research establishes that the maximal generated power in a heat engine operating under slow driving corresponds to the optimal ratio between an effective area weighted by the Berry curvature associated with pumping and the thermodynamic length defined by the metric associated with dissipation.

Qubit Interactions Bypass Landauer-Like Heat Limits

This research presents a detailed analysis of thermal machines operating with interacting qubits, advancing the field of quantum thermodynamics. Scientists developed a systematic method, based on the Lindblad master equation and a slow-driving expansion, to calculate key quantities such as work, heat currents, and entropy production. This approach successfully separates geometric and dissipative contributions to the process, identifying a connection to Berry curvature and a metric in the parameter space of the driving forces. The results demonstrate that the amount of heat pumped per cycle is linked to a fundamental limit, analogous to the Landauer limit for entropy change, but this bound can be overcome through qubit interactions and asymmetric coupling to thermal reservoirs.

Investigations into a two-qubit system reveal the significant role of both qubit interactions and their coupling to the surrounding environment in determining the overall power dissipation. This work establishes a general framework for studying energy dissipation, pumping, and performance optimisation in quantum devices functioning as heat engines. The authors acknowledge that their analysis relies on the slow-driving approximation, limiting its direct applicability to faster operating regimes, and future research will explore many-qubit systems and stronger system-bath couplings.