The Szilard engine is a foundational thought experiment that rigorously links thermodynamicsand information theory. With the miniaturization of devices and ongoingprogress in quantum information science, it is crucial to examine how quantumeffects influence the operation of such engines. This thesis investigates the finitetimedynamics of a quantum Szilard engine subjected to size-invariant shape transformations,in which the geometry of the confinement potential is deformed withoutaltering its overall size. The system’s evolution is modeled using a time-dependent,Markovian LGKS (Lindblad-Gorini-Kossakowski-Sudarshan) master equation. Wenumerically solve this equation to analyze the thermodynamic behavior of the engine,focusing on the roles of quantum coherence and its interplay with heat, work,and entropy throughout the cycle. Special attention is given to how coherenceevolves under varying barrier insertion rates and thermalization temperatures. Wedemonstrate that coherence generation is strongly influenced by both the protocolspeed and the bath temperature. Furthermore, we show a connection between coherenceaccumulation and the energetic and informational cost of the cycle. Thesefindings enhance our understanding of coherence in finite-time, measurement-basedquantum devices and suggest that geometric deformations can serve as a powerfultool for thermodynamic control in quantum technologies.
The Szilard engine is a foundational thought experiment that rigorously links thermodynamicsand information theory. With the miniaturization of devices and ongoingprogress in quantum information science, it is crucial to examine how quantumeffects influence the operation of such engines. This thesis investigates the finitetimedynamics of a quantum Szilard engine subjected to size-invariant shape transformations,in which the geometry of the confinement potential is deformed withoutaltering its overall size. The system’s evolution is modeled using a time-dependent,Markovian LGKS (Lindblad-Gorini-Kossakowski-Sudarshan) master equation. Wenumerically solve this equation to analyze the thermodynamic behavior of the engine,focusing on the roles of quantum coherence and its interplay with heat, work,and entropy throughout the cycle. Special attention is given to how coherenceevolves under varying barrier insertion rates and thermalization temperatures. Wedemonstrate that coherence generation is strongly influenced by both the protocolspeed and the bath temperature. Furthermore, we show a connection between coherenceaccumulation and the energetic and informational cost of the cycle. Thesefindings enhance our understanding of coherence in finite-time, measurement-basedquantum devices and suggest that geometric deformations can serve as a powerfultool for thermodynamic control in quantum technologies.
We analyze an engine whose working fluid consists of a single quantum particle, paralleling Szilard's construction of a classical single-particle engine. Following his resolution of Maxwell's Second Law paradox using the latter, which turned on physically instantiating the demon (control subsystem), the quantum engine's design mirrors the classically-chaotic Szilard Map that operates a thermodynamic cycle of measurement, thermal-energy extraction, and memory reset. Focusing on the thermodynamic costs to observe and control the particle and comparing these in the quantum and classical limits, we detail the thermodynamic tradeoffs behind Landauer's Principle for information-processing-induced thermodynamic dissipation in the quantum and classical regimes. In particular, and as found with the classical engine, we show that the sum of the thermodynamic costs over a cycle obeys a generalized Landauer Principle, exactly balancing energy extraction from the heat bath. Thus, the quantum engine obeys the Second Law. However, the quantum engine does so via substantially different mechanisms: classically measurement and erasure determine the thermodynamics, while in the quantum implementation the cost of partition insertion is key.
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.
The emergence of irreversibility in physical processes, despite the fundamentally reversible nature of quantum mechanics, remains an open question in physics. This thesis explores the intricate relationship between quantum mechanics and thermodynamics, with a particular focus on minimizing entropy production in finite-time processes. By employing tools from quantum information theory and geometric thermodynamics, we tackle the challenge of deriving irreversible thermodynamic behavior from the reversible microscopic framework of quantum mechanics. We begin with a comprehensive review of the laws of thermodynamics, setting the stage for the subsequent analyses. We introduce novel developments in quantum thermodynamics through a generalized framework for geometric thermodynamics, which enables the derivation of finite-time corrections beyond the Markovian regime. Building on this foundation, we extend Landauer's principle by incorporating a finite-time correction that highlights the necessity of strong coupling for optimal information erasure processes. This result underscores the emergence of Planckian time as a fundamental speed limit to thermalization. Additionally, we explore how collective effects can be harnessed to reduce energy dissipation in thermodynamic operations, revealing that classical correlations between systems can significantly mitigate dissipation, though this may pose new questions regarding the third law of thermodynamics. Finally, we optimize thermodynamic processes in mesoscopic systems, including quantum dot engines and information engines. These findings not only enhance our understanding of the fundamental limits of irreversibility but also open new avenues for research. Future works will focus on fully exploiting collective effects, aligning these with the third law of thermodynamics, and understanding the thermodynamic consistency of master equations.
We investigate a finite-time quantum Otto engine within the framework of gauge-invariant quantum thermodynamics, using the Lipkin-Meshkov-Glick model as the working medium. In this formulation, thermodynamic quantities are defined on equivalence classes of thermodynamically indistinguishable states, leading naturally to gauge-invariant notions of work, heat, entropy, and efficiency. We derive explicit expressions for these quantities and show that the usual work performed during the unitary strokes decomposes into an invariant contribution, associated with changes in the instantaneous energy spectrum and populations, and a coherent contribution arising from finite-time quantum coherences. This decomposition induces the corresponding splittings of engine efficiency and entropy production, providing a geometric interpretation of finite-time irreversibility and clarifying the role of coherence in work extraction. By analyzing the cycle's dependence on driving speed and system size, we identify the engine's operating region and investigate the influence of criticality. We show that crossing the critical region substantially reduces the parameter space in which the cycle operates as a heat engine. At the same time, whenever the engine condition remains satisfied, the discrepancy between the conventional and gauge-invariant descriptions becomes strongly suppressed, indicating that the gauge-invariant sector predominantly carries the extracted work. These results establish a direct connection between gauge-invariant thermodynamics, finite-time irreversibility, and work extraction in many-body quantum thermal machines.
Abstract The so-called information-thermodynamics link created by a thought experiment of Szilard became a core of modern orthodoxy in the field of quantum information and resources theory in quantum thermodynamics. We recall existing objections against standard interpretation of Szilard engine operation and illustrate them by two quantum models: a particle in a box with time-dependent thin potential barrier and the spin-boson model. The consequences of the emerging superselection rules for thermodynamics and foundations of quantum mechanics are discussed. The role of non-ergodic systems as information carriers and the thermodynamic cost of stability and accuracy of information processing is briefly discussed and compared to the generally accepted Landauer’s principle.
We study the physical mechanism of Maxwell's demon (MD), which helps do extra work in thermodynamic cycles with the heat engine. This is exemplified with one molecule confined in an infinitely deep square potential with a movable solid wall. The MD is modeled as a two-level system (TLS) for measuring and controlling the motion of the molecule. The processes in the cycle are described in a quantum fashion. It is discovered that a MD with quantum coherence or one at a temperature lower than the molecule's heat bath can enhance the ability of the whole working substance, formed by the heat engine plus the MD, to do work outside. This observation reveals that the essential role of the MD is to drive the whole working substance off equilibrium, or equivalently, to work between two heat baths with different effective temperatures. The elaborate studies with this model explicitly reveal the effect of finite size off the classical limit or thermodynamic limit, which contradicts common sense on a Szilard heat engine (SHE). The quantum SHE's efficiency is evaluated in detail to prove the validity of the second law of thermodynamics.