The interplay between heat flow and information processing has long been a frontier of both statistical physics and quantum information science. In this work we propose that during thermal evolution of a quantum many‑body system, an otherwise hidden conservation law emerges, which we denote as the Thermal Information Conservation Law (TIC). This law is encapsulated in the invariant quantity \(Q_T\), defined as a functional of the system's density matrix and local observables, and remains constant under unitary evolution that couples to a thermal bath only through weak, Markovian channels. The existence of \(Q_T\) imposes stringent constraints on the allowed thermal trajectories, thereby providing a new lens through which to view irreversibility, entropy production, and the emergence of classical thermodynamic behavior from quantum dynamics. By establishing a rigorous bridge between the traditional Clausius inequality and a quantum‑information‑theoretic monotone, we demonstrate that TIC can be leveraged to quantify the ultimate limits of heat‑to‑work conversion in quantum engines and to design protocols that suppress entropy generation. The potential Nobel‑worthy significance of this finding lies in its unification of two seemingly disparate domains: the macroscopic laws of thermodynamics and the microscopic rules of quantum information theory. The paper is organized as follows: Section 1 introduces the conceptual framework; Section 2 formalizes the definition of \(Q_T\) and proves its conservation under specified conditions; Section 3 discusses the implications for quantum thermodynamics; Section 4 explores connections to quantum information measures such as mutual information and quantum discord; Section 5 outlines theoretical pathways for experimental verification; Section 6 presents a discussion of limitations and future directions; and Section 7 concludes the study.
The interplay between heat flow and information processing has long been a frontier of both statistical physics and quantum information science. In this work we propose that during thermal evolution of a quantum many‑body system, an otherwise hidden conservation law emerges, which we denote as the Thermal Information Conservation Law (TIC). This law is encapsulated in the invariant quantity (Q_T), defined as a functional of the system's density matrix and local observables, and remains constant under unitary evolution that couples to a thermal bath only through weak, Markovian channels. The existence of (Q_T) imposes stringent constraints on the allowed thermal trajectories, thereby providing a new lens through which to view irreversibility, entropy production, and the emergence of classical thermodynamic behavior from quantum dynamics. By establishing a rigorous bridge between the traditional Clausius inequality and a quantum‑information‑theoretic monotone, we demonstrate that TIC can be leveraged to quantify the ultimate limits of heat‑to‑work conversion in quantum engines and to design protocols that suppress entropy generation. The potential Nobel‑worthy significance of this finding lies in its unification of two seemingly disparate domains: the macroscopic laws of thermodynamics and the microscopic rules of quantum information theory. The paper is organized as follows: Section 1 introduces the conceptual framework; Section 2 formalizes the definition of (Q_T) and proves its conservation under specified conditions; Section 3 discusses the implications for quantum thermodynamics; Section 4 explores connections to quantum information measures such as mutual information and quantum discord; Section 5 outlines theoretical pathways for experimental verification; Section 6 presents a discussion of limitations and future directions; and Section 7 concludes the study.
The concept of thermal information conservation offers a new perspective on the interplay between thermodynamics and quantum information theory. In this work we introduce the thermal information quantity Q_T, defined for an isolated quantum system as the negative logarithm of the density of states weighted by the Boltzmann factor. We demonstrate that Q_T behaves as a conserved quantity during unitary evolution under a broad class of Hamiltonians that respect a hidden symmetry connecting energy and entropy. By establishing a rigorous link between Q_T and the von Neumann entropy, we show that the standard second law of thermodynamics can be viewed as a special case of a more general conservation principle. The implications of this principle for the design of quantum thermal engines, error‑free quantum memory, and the fundamental limits of heat transport are discussed. The framework also provides a natural bridge between classical thermodynamic irreversibility and quantum reversibility, suggesting that the apparent arrow of time in macroscopic systems may emerge from constraints on Q_T rather than from entropy production alone. Keywords: Thermal information, quantum thermodynamics, conservation law, entropy, quantum engines.
We formulate a geometric framework in which physical laws emerge from restricted access to microscopic information. Measurement constraints are modeled as a gauge symmetry acting on density operators, inducing a gauge-reduced space of physically distinguishable states. In the case of quantum thermodynamics, this construction leads to a gauge-invariant formulation in which the invariant entropy admits a stochastic description and satisfies a general detailed fluctuation theorem. From this result, we derive an integrated fluctuation theorem and a Clausius-like inequality that unifies the first and second laws in terms of invariant work and coherent heat. Entropy production is identified with the relative entropy between forward and backward probability measures on the gauge-reduced space of thermodynamic trajectories, revealing irreversibility as a geometric consequence of limited observability. The third law emerges as a singular zero-temperature limit in which thermodynamic orbits collapse and entropy production vanishes. Since the framework applies to arbitrary information constraints, it encompasses energy-based thermodynamics as a particular case of more general measurement scenarios.
To understand in detail the relation between unitary quantum theory that describes our world at the microscopic scale and thermodynamics, which was long believed only to apply to macroscopic objects, is one of the most interesting and long-standing problems in physics. Recently, this problem has received renewed attention, in particular from the community of quantum information theory, but also from the field of statistical mechanics, inspired from stochastic thermodynamics. These results suggest that thermodynamics is also relevant for individual quantum systems, provided that they can be brought into contact with thermal baths. In this thesis, I use recently developed tools to provide new results both on fundamental questions, but also on questions which are of practical relevance for potential miniaturized thermal machines. In terms of fundamental questions, the results in this thesis contribute to understanding how the basic laws of thermodynamics and statistical mechanics can be understood directly from unitary quantum mechanics. In particular, I discuss and answer the following questions: i) How can we quantify the third law of thermodynamics using information theoretic methods? ii) How can we quantify the "thermodynamic value" of a state-transition in quantum systems? iii) How can we axiomatically characterize the non-equilibrium free energy and relative entropy? iv) How can we justify statistical ensembles from an operational perspective, without having to introduce either some probability measures or an information theoretic entropy measure? v) How can we understand the equilibration of closed quantum systems, how long does it take and how difficult is it to avoid? In the second part of the thesis I discuss in detail how experimental restrictions, which become important at the quantum scale, influence the ultimate thermodynamic bounds for thermal machines. In particular, the results in this thesis provide thermodynamic bounds on work-extraction and efficiencies of thermal machines in situations where 1.) an experimenter only has limited field strengths available, 2.) an experimenter cannot control the interactions between particles, but external fields arbitrarily well, and 3.) situations in which a small quantum system can only be strongly coupled to heat baths. These bounds are tight and I provide explicit examples illustrating the different behaviours. Finally, I come back to a classic problem in statistical physics: The emergence of spontaneous symmetry breaking. Here, I provide general and rigorous new results that show how symmetry-breaking stationary states emerge from fluctuations in order parameters in dissipative lattice models.
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.
A central open question in quantum thermodynamics is the identification of thermodynamic entropy away from equilibrium. Although thermodynamic entropy coincides with the von Neumann entropy for a Gibbs state at equilibrium, the thermodynamic role of quantum coherence generated during nonequilibrium evolution remains unclear. Here, we show that von Neumann entropy does not, in general, represent the thermodynamic entropy governing heat exchange in coherent nonequilibrium quantum systems. By integrating the resource theory of quantum coherence with thermodynamic principles, we develop a general framework for nonequilibrium quantum thermodynamics. We identify thermodynamic entropy with the energy entropy derived from energy-measurement statistics and introduce a dynamical temperature extending the equilibrium concept to nonequilibrium states. Consequently, we obtain an exact entropy-balance relation separating the entropy flux associated with heat exchange from the coherence-loss contribution to entropy production, establishing an operational connection between quantum coherence, heat flow, and total entropy change. Unlike approaches relying on equilibrium reference states or stationary Gibbs ensembles, our framework uses instantaneous dynamical quantities and remains valid throughout transient nonequilibrium evolution. It provides consistent dynamical definitions of temperature, work, heat, and free energy. Applying the formalism to an exactly solvable open quantum system, we show that the first and second laws hold throughout transient evolution and that equilibrium thermodynamics emerges dynamically in the weak-coupling long-time limit. Our results establish a unified framework for coherent nonequilibrium quantum thermodynamics and suggest opportunities for controlling heat dissipation through coherence engineering in quantum thermal technologies.
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.