Identifying general links between energetics and information in realistic open quantum systems is a long-standing problem in quantum thermodynamics and quantum information processing. However, the generality of existing efforts is often impeded by their specific assumptions about environments. Here we address the problem by developing a trajectory-level thermodynamic inference theory to establish general links using just the knowledge of the system, enabling a single framework applicable to a diverse range of environments. Underpinning the framework is a notion of excess energy introduced for inferring the net energy gain of the system after completing an information processing trajectory. We show that fluctuation behaviors of the excess energy encode general links between energetics and information with a conceptual advantage that they completely avoid assumptions about environments and system-environment coupling forms. Crucially, we obtain a single thermodynamic inequality that integrates upper bounds on heat dissipation and extracted work in terms of system's information content change, providing complementary constraints that greatly expand the context of existing well-adopted results based on the second law of thermodynamics. We also uncover lower bounds on the precision of the fluctuating system's energy and information content changes in terms of their Fano factors and a correlation function between them. By extending relations between energetics and information to higher-order fluctuations, we thus reveal a trade-off that a more precise inference of energy or information content changes requires a looser energetic-information link. We showcase the implications of these general links in a number of quantum information and thermodynamic tasks of application relevance. Our framework provides a toolkit for analyzing the interplay between energetics and information from the trajectory level in generic quantum systems, thereby adding an indispensable structure to the thermodynamics of information. Published by the American Physical Society 2024
Identifying general links between energetics and information in realistic open quantum systems is a long-standing problem in quantum thermodynamics and quantum information processing. However, the generality of existing efforts is often impeded by their specific assumptions about environments. Here we address the problem by developing a trajectory-level thermodynamic inference theory to establish general links using just the knowledge of the system, enabling a single framework applicable to a diverse range of environments. Underpinning the framework is a notion of excess energy introduced for inferring the net energy gain of the system after completing an information processing trajectory. We show that fluctuation behaviors of the excess energy encode general links between energetics and information with a conceptual advantage that they completely avoid assumptions about environments and system-environment coupling forms. Crucially, we obtain a single thermodynamic inequality that integrates upper bounds on heat dissipation and extracted work in terms of system's information content change, providing complementary constraints that greatly expand the context of existing well-adopted results based on the second law of thermodynamics. We also uncover lower bounds on the precision of the fluctuating system's energy and information content changes in terms of their Fano factors and a correlation function between them. By extending relations between energetics and information to higher-order fluctuations, we thus reveal a trade-off that a more precise inference of energy or information content changes requires a looser energetic-information link. We showcase the implications of these general links in a number of quantum information and thermodynamic tasks of application relevance. Our framework provides a toolkit for analyzing the interplay between energetics and information from the trajectory level in generic quantum systems, thereby adding an indispensable structure to the thermodynamics of information. Published by the American Physical Society 2024
The Landauer's principle, a cornerstone of information thermodynamics, provides a fundamental lower bound on the energetic cost of information erasure in terms of the information content change. However, its traditional formulation is largely confined to systems exchanging solely energy with an ideal thermal bath. In this work, we derive general information-cost trade-off relations that go beyond the scope of Landauer's principle by developing a thermodynamic inference approach based on the maximum entropy principle. These relations require only information about the system and are applicable to complex quantum scenarios involving multiple conserved charges and non-thermal environments. Specifically, we present two key results: (i) In scenarios where only the mean values of observables are accessible, we derive an information-content-informed upper bound on the thermodynamic cost which complements an existing generalized Landauer lower bound. (ii) When second-order fluctuations can also be measured, we obtain an information-content-informed lower bound on the change in variances of observables, thereby extending the Landauer's principle to constrain higher-order fluctuation costs. We numerically validate our information-cost trade-off relations using a coupled-qubit system exchanging energy and excitations, a driven qubit implementing an information erasure process, and a driven double quantum dot system that can operate as an inelastic heat engine. Our results underscore the broad utility of maximum-entropy inference in constraining thermodynamic costs for generic finite-time quantum processes, with direct relevance to quantum information processing and quantum thermodynamic applications.
The thermodynamical behavior of quantum systems at the nanoscale is often very difficult to capture via standard frameworks of thermodynamics. The latter is, in fact, an equilibrium theory whose predictions are typically only valid on average, and in regimes where systems are composed of a very large number of constituents. In reality, the thermodynamical behavior of nanoscale systems can be much more constrained that what is predicted by macroscopic thermodynamics, due to the unavoidable impact of fluctuations. As a result, the fundamental limitations to a system's dynamics induced by macroscopic thermodynamics might turn out to be considerably less stringent than what can actually be observed at those scales. The theory of open quantum systems is certainly a powerful tool in this context, and can provide solutions which go beyond equilibrium treatments, but solving the dynamics of an open system requires detailed information about its microscopic structure (e.g. system-environment interactions and coupling strengths). In other words, one of the great advantages of macroscopic thermodynamics, i.e. its universality and independence of microscopic details, might be essentially lost if we can only infer thermodynamical results once we specify the full microscopic structure of our system-environment interaction. This highlights the necessity for a framework of thermodynamics that is well suited for studying the behavior of small quantum systems far from equilibrium, but can still be applied to physical systems in a universal way, i.e., without having to specify full microscopic information. Quantum Resource Theories (QRTs), and in particular the formulations of quantum thermodynamics that have emerged from them, constitute a promising tool in this direction. However, these models of thermodynamics have not yet been extensively applied to realistic physical platform, and their consequences on known thermodynamical processes are still unexplored. Furthermore, going beyond a purely thermodynamical context, a case can be made for the use of general QRTs as benchmarking tools for the certification of certain quantum resources. In other words, QRTs could be used to find fundamental bounds to physical quantities or impossibility results (in the form of no-go theorems) that, when compared to experimental data, can be used to falsify specific hypotheses. In this thesis, both these directions will be explored, by considering resource-theoretical questions that are relevant for different physical platforms. These will include the photochemical process of photoisomerization, heat transport in harmonic systems, and tabletop tests of quantum gravity.
Abstract Establishing a concrete link between quantum information measures and thermodynamic quantities remains a significant challenge in contemporary research. This paper presents novel contributions exploring three key aspects. First, we investigate the relationship between quantum Fisher information (QFI) and work and heat exchange during a feedback control measurement cycle, unveiling a quantitative interplay between energy and information. Second, we demonstrate the behavior of heat exchange with the environment at the point of maximum estimation precision, and a direct relation that links the von Neumann entropy in systems with a large number of microstates with the precision of the estimation through QFI, shedding light on the thermodynamic signature of optimal quantum parameter estimation, bridging quantum metrology, and statistical thermodynamics in the context of high-dimensional stochastic systems. Finally, we propose a method for detecting entanglement based on thermodynamic work, introducing a framework to identify entanglement through energy considerations in a quantum system. Together, these findings advance our understanding of the intersection between quantum information theory and quantum thermodynamics, providing an additional foundation for future research.
Thermodynamics and information have intricate interrelations. Often thermodynamics is considered to be the logical premise to justify that information is physical - through Landauer's principle -, thereby also linking information and thermodynamics. This approach towards information has been instrumental to understand thermodynamics of logical and physical processes, both in the classical and quantum domain. In the present work, we formulate thermodynamics as an exclusive consequence of information conservation. The framework can be applied to the most general situations, beyond the traditional assumptions in thermodynamics: we allow systems and thermal baths to be quantum, of arbitrary sizes and even possessing inter-system correlations.Here, systems and baths are not treated differently, rather both are considered on an equal footing. This leads us to introduce a ''temperature''-independent formulation of thermodynamics. We rely on the fact that, for a fixed amount of information, measured by the von Neumann entropy, any system can be transformed to a state with the same entropy that possesses minimal energy. This state, known as a completely passive state, acquires Boltzmann-Gibbs canonical form with an intrinsic temperature . We introduce the notions of bound and free energy and use them to quantify heat and work, respectively. Guided by the principle of information conservation, we develop universal notions of equilibrium, heat and work, Landauer's principle and universal fundamental laws of thermodynamics. We demonstrate that the maximum efficiency of a quantum engine with a finite bath is in general lower than that of an ideal Carnot engine. We introduce a resource theoretic framework for our intrinsic temperature based thermodynamics, within which we address the problem of work extraction and state transformations. Finally, the framework is extended to multiple conserved quantities.
Thermodynamics and information have intricate interrelations. Often thermodynamics is considered to be the logical premise to justify that information is physical - through Landauer's principle -, thereby also linking information and thermodynamics. This approach towards information has been instrumental to understand thermodynamics of logical and physical processes, both in the classical and quantum domain. In the present work, we formulate thermodynamics as an exclusive consequence of information conservation. The framework can be applied to the most general situations, beyond the traditional assumptions in thermodynamics: we allow systems and thermal baths to be quantum, of arbitrary sizes and even possessing inter-system correlations.Here, systems and baths are not treated differently, rather both are considered on an equal footing. This leads us to introduce a ''temperature''-independent formulation of thermodynamics. We rely on the fact that, for a fixed amount of information, measured by the von Neumann entropy, any system can be transformed to a state with the same entropy that possesses minimal energy. This state, known as a completely passive state, acquires Boltzmann-Gibbs canonical form with an intrinsic temperature. We introduce the notions of bound and free energy and use them to quantify heat and work, respectively. Guided by the principle of information conservation, we develop universal notions of equilibrium, heat and work, Landauer's principle and universal fundamental laws of thermodynamics. We demonstrate that the maximum efficiency of a quantum engine with a finite bath is in general lower than that of an ideal Carnot engine. We introduce a resource theoretic framework for our intrinsic temperature based thermodynamics, within which we address the problem of work extraction and state transformations. Finally, the framework is extended to multiple conserved quantities.
Originally formulated for macroscopic machines, the laws of thermodynamics were recently shown to hold for quantum systems coupled to ideal sources of work (external classical fields) and heat (systems at equilibrium). Ongoing efforts have been focusing on extending the validity of thermodynamic laws to more realistic, non-ideal energy sources. Here, we go beyond these extensions and show that energy exchanges between arbitrary quantum systems are structured by the laws of thermodynamics. We first generalize the second law and identify the associated work and heat exchanges. After recovering known results from ideal work and heat sources, we analyze some consequences of hybrid work and heat sources. We illustrate our general laws with microscopic machines realizing thermodynamic tasks in which the roles of heat and work sources are simultaneously played by elementary quantum systems. Our results open perspectives to understand and optimize the energetic performances of realistic quantum devices, at any scale.