Description: In the context of quantum thermodynamics the Landauer's principle and the Szilard engine are usually presented as the paradigmatic examples of the inter-convertibility between information and work. Besides, the fluctuation-dissipation theorems (Jarzynski and Crooks equalities) take into account the quantum effects in work extraction. By means of resource theoretic tools, we aim to develop a framework that unifies all the above phenomena as manifestations of the same fundamental principle: quantum channels with energy conservation constraints.
Description: In the context of quantum thermodynamics the Landauer's principle and the Szilard engine are usually presented as the paradigmatic examples of the inter-convertibility between information and work. Besides, the fluctuation-dissipation theorems (Jarzynski and Crooks equalities) take into account the quantum effects in work extraction. By means of resource theoretic tools, we aim to develop a framework that unifies all the above phenomena as manifestations of the same fundamental principle: quantum channels with energy conservation constraints.
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.
This paper presents a comprehensive exposition of quantum thermodynamics, aiming to bridge the foundational concepts of classical thermodynamics and quantum mechanics.Beginning with a rigorous overview of classical thermodynamic laws and statistical ensembles, the work transitions into the quantum domain by introducing quantum states, density operators, and von Neumann entropy.Core thermodynamic quantities such as work, heat, energy, and entropy are redefined in the quantum regime, with emphasis on operational frameworks like the twopoint measurement scheme.The study explores the role of quantum resource theories in formulating generalizations of the second law and delves into the intricacies of nonequilibrium thermodynamics through fluctuation theorems, such as the Jarzynski equality and Crooks theorem.Special attention is given to the influence of coherence, entanglement, and measurement backaction, which contribute uniquely to quantum thermodynamic behavior.The treatise concludes with a discussion on quantum heat engines, thermodynamic consistency of quantum master equations, and information-theoretic approaches, establishing quantum thermodynamics as a vital framework for understanding energy and information flow at the quantum scale.
In a classic thought experiment, Szilard suggested a heat engine where a single particle, for example an atom or a molecule, is confined in a container coupled to a single heat bath. The container can be separated into two parts by a moveable wall acting as a piston. In a single cycle of the engine, work can be extracted from the information on which side of the piston the particle resides. The work output is consistent with Landauers principle that the erasure of one bit of information costs the entropy kB ln 2, exemplifying the fundamental relation between work, heat and information. Here we apply the concept of the Szilard engine to a fully interacting quantum many-body system. We find that a working medium of a number of bosons (larger or equal two) with attractive interactions is clearly superior to other previously discussed setups. In sharp contrast to the classical case, we find that the average work output increases with the particle number. The highest overshoot occurs for a small but finite temperature, showing an intricate interplay between thermal and quantum effects. We anticipate that our finding will shed new light on the role of information in controlling thermodynamic fluctuations in the deep quantum regime, which are strongly influenced by quantum correlations in interacting systems.
We present a critical examination of the difficulties with the quantum versions of a lifted weight that are widely used as work storage systems in quantum thermodynamics. To overcome those difficulties, we turn to the strong connections between information and thermodynamics illuminated by Szilard’s engine and Landauer’s principle, and consider the concept of informational work storage. This concept is in sharp contrast with the usual one of mechanical work storage underlying the idealization of a quantum weight. An informational work storage system based on maximally mixed qubits that does not act as an entropy sink and is capable of truly distinguishing work from heat is studied. Applying it to the problem of single-shot work extraction in various extraction schemes, we show that for a given system state the maximum extractable work is independent of extraction scheme, in accordance with the second law of thermodynamics.
It is often claimed, that from a quantum system of d levels, and entropy S and heat bath of temperature T one can draw kT lnd–TS amount of work. However, the usual arguments basing on Szilard engine, are not fully rigorous. Here we prove the formula within Hamiltonian description of drawing work from a quantum system and a heat bath, at the cost of entropy of the system. We base on the derivation of thermodynamical laws and quantities in [10] within weak coupling limit. Our result provides fully physical scenario for extracting thermodynamical work form quantum correlations [4]. We also derive Landauer's principle as a consequence of the second law within the considered model.