In this study, we uncover the intrinsic information processes in non-Hermitian quantum systems and their thermodynamic effects. We demonstrate that these systems can exhibit negative entropy production, making them potential candidates for information engines. We also identify a key informational quantity that can characterize phase transitions beyond the reach of traditional partition functions. This work enhances our understanding of the interplay between information and thermodynamics, providing a new perspective on non-Hermitian quantum systems.
In this study, we uncover the intrinsic information processes in non-Hermitian quantum systems and their thermodynamic effects. We demonstrate that these systems can exhibit negative entropy production, making them potential candidates for information engines. We also identify a key informational quantity that can characterize phase transitions beyond the reach of traditional partition functions. This work enhances our understanding of the interplay between information and thermodynamics, providing a new perspective on non-Hermitian quantum systems.
We develop a first-principles thermodynamic framework for non-Hermitian dynamics based on a post-selected version of the fluctuation theorem. This allows us to identify a quantity that remains positive throughout the non-Hermitian evolution and can be interpreted as the entropy production of the post-selected dynamics. We relate this quantity to previously proposed notions of non-Hermitian entropy and derive an associated second law. Furthermore, we establish a connection with information-theoretic quantities, in particular the Petz-Rényi divergences, and leverage this connection to derive upper and lower bounds. Finally, we decompose the entropy production into incoherent and coherent contributions, identifying distinctive features of the coherent term in the vicinity of exceptional points. We illustrate our results using a paradigmatic model of non-Hermitian evolution based on a two-level system.
Traditional thermodynamics, built upon the foundation of Hermitian quantum mechanics, primarily describes closed or weakly open systems where energy is conserved. However, the ubiquitous presence of dissipation and gain in realistic physical and biological systems necessitates a more generalized framework. Non-Hermitian quantum mechanics, characterized by Hamiltonians with complex eigenvalues, naturally accounts for such open systems and their interaction with the environment. This paper explores the burgeoning field of non-Hermitian thermodynamics, which aims to extend classical and quantum thermodynamic principles to systems exhibiting energy exchange with their surroundings. We delve into how non-Hermiticity provides a natural language for describing processes involving dissipation, gain, and decoherence, thereby offering a unified perspective on these phenomena. Key concepts such as PT-symmetry, exceptional points, and generalized definitions of work, heat, and entropy in non-Hermitian settings are reviewed. The paper discusses the implications for fundamental thermodynamic laws, the performance of non-Hermitian heat engines, and the role of coherence in energy transport. By embracing the mathematical elegance and physical insights of non-Hermitian physics, we propose a comprehensive framework that unifies the seemingly disparate concepts of dissipation and coherence within a consistent thermodynamic theory, paving the way for advanced applications in quantum technologies, materials science, and biological energy transfer.
This paper explores the emerging intersection of quantum thermodynamics and quantum information processing. The core argument presented is that quantum information processing fundamentally relies on the thermodynamic properties of quantum systems and can be significantly advanced by leveraging the principles of quantum thermodynamics. This work establishes a framework for analyzing and designing quantum information protocols through the lens of thermodynamic constraints and efficiencies. We introduce a novel perspective where quantum information tasks are viewed as thermodynamic processes, allowing for a more rigorous understanding of their limitations and potential optimizations. The methodology presented aims to bridge the gap between information theory and thermodynamics, ultimately leading to the development of more robust and efficient quantum information systems. Key concepts explored include quantum work, heat dissipation, entropy production, and their implications for quantum data storage, quantum computation, and quantum communication. This research contributes to a fundamental shift in how we approach quantum information processing, moving beyond purely computational considerations to incorporate the underlying thermodynamic realities of quantum systems.
The thermodynamics of quantum phase transitions has long been a rich area of research, providing numerous insights and enhancing our understanding of this important phenomenon. This theoretical framework has been well developed specially because quantum phase transitions occur at equilibrium. However, its dynamical counterpart, known as dynamical quantum phase transitions, takes place out of equilibrium, where conventional thermodynamic tools are inapplicable. In this work we make progress in this area by connecting dynamical criticality to thermodynamics through a geometric perspective on entropy production. Our findings, along with other recent developments, suggest that dynamical criticality can lead the system to highly complex dynamics, indicating a possible pathway to thermalization.
The study of quantum criticality has historically been confined to Hermitian systems, where closed-system approximations neglect environmental interactions. However, a significant portion of quantum phenomena occurs in open systems, necessitating a departure from this conventional framework. This paper explores non-Hermitian quantum criticality in open many-body systems, delving into the unique phases and phase transitions that emerge due to dissipation, gain, and other non-conservative interactions. We establish a comprehensive framework that integrates concepts from biorthogonal quantum mechanics, Liouvillian dynamics, and tensor network methods to characterize critical phenomena, including dynamical quantum phase transitions and the emergence of non-Hermitian quantum many-body scars. Through an extensive literature review, we highlight how the interplay of non-Hermiticity with many-body correlations leads to novel critical behaviors, distinct from their Hermitian counterparts, and in some cases, surprisingly resilient or even enhanced. We discuss the role of exceptional points as hallmarks of non-Hermitian systems, their influence on energy spectra, and their implications for criticality and topological invariants. Furthermore, we examine the methodologies for defining observables and statistical ensembles in these non-Hermitian settings, emphasizing the distinctions and occasional controversies that arise. The findings provide critical insights into the fundamental principles governing quantum criticality in dissipative environments and pave new avenues for engineering and understanding open quantum technologies, from quantum sensing to robust quantum information processing.
Abstract Entropy production plays a pivotal role in characterizing the inherent irreversibility of non-equilibrium quantum processes, and a thorough understanding of this concept holds immense potential for advancing the design of thermodynamically efficient quantum technologies. In this work, we demonstrate that the entropy production observed in multipartite open quantum systems, undergoing independent dissipations, arises from two sources: the local dynamics governing individual subsystems and the non-local correlations embedded within the system. The contributions of quantum correlations, as genuine quantum effects, to entropy production are identified explicitly. The revelation of the source of entropy production is substantiated by an analysis of its stochastic counterpart, derived from quantum trajectories. Furthermore, we propose an experimentally feasible scheme to isolate the contributions of both classical and quantum correlations to entropy production. The theoretical findings are simulated using an optical setup. Our work establishes a profound connection between thermodynamic and informational quantities, elucidating the source of irreversibility in the non-equilibrium process of multipartite quantum systems and the genuine quantum contribution therein.