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Quantum Correlation Heat Capacity: A Novel Thermodynamic Paradigm

Jincheng Zhang

Published Aug 11, 2026• 0 citations
Publisher

Abstract

This paper introduces the concept of Quantum Correlation Heat Capacity (QCHC), denoted as C_corr, as an independent thermodynamic response function characterizing the temperature-dependent evolution of quantum correlations within multipartite systems. While traditional thermodynamics defines heat capacity solely through the lens of internal energy variations with respect to temperature, namely C = (partial E) / (partial T), the framework presented here posits that information-theoretic measures—specifically quantum mutual information I(A:B)—exhibit their own distinct thermal storage and transfer dynamics. We define the quantum correlation heat capacity as C_corr = T * (partial I(A:B)) / (partial T), capturing the rate at which quantum correlation energy or informational configuration changes per unit temperature shift. By bridging quantum information theory and statistical mechanics, we demonstrate that temperature variations can induce an independent correlation heat storage capacity that operates orthogonally to ordinary energetic degrees of freedom. This formulation expands the conventional set of thermodynamic state variables, offering profound implications for quantum thermodynamics, information erasure, and the foundations of statistical mechanics.

DOI
10.5281/zenodo.21885282

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This paper introduces the concept of Quantum Correlation Heat Capacity (QCHC), denoted as C_corr, as an independent thermodynamic response function characterizing the temperature-dependent evolution of quantum correlations within multipartite systems. While traditional thermodynamics defines heat capacity solely through the lens of internal energy variations with respect to temperature, namely C = (partial E) / (partial T), the framework presented here posits that information-theoretic measures—specifically quantum mutual information I(A:B)—exhibit their own distinct thermal storage and transfer dynamics. We define the quantum correlation heat capacity as C_corr = T * (partial I(A:B)) / (partial T), capturing the rate at which quantum correlation energy or informational configuration changes per unit temperature shift. By bridging quantum information theory and statistical mechanics, we demonstrate that temperature variations can induce an independent correlation heat storage capacity that operates orthogonally to ordinary energetic degrees of freedom. This formulation expands the conventional set of thermodynamic state variables, offering profound implications for quantum thermodynamics, information erasure, and the foundations of statistical mechanics.
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We extend the Carathéodory principle of the second law to quantum thermodynamics, where energy levels depend on macroscopic variables such as volume and magnetic field. This extension introduces the concept of quantum thermodynamic integrability (QTI), providing an alternative foundation for statistical mechanics. QTI is characterized by the path independence of work and heat within the thermodynamic manifold, locally described by energy levels and specific thermodynamic parameters. Within this framework, temperature naturally emerges as an integrating factor, enabling the derivation of both canonical and noncanonical states from the entropy integrable equations based on QTI. Notably, noncanonical states, which become particularly significant outside the thermodynamic limit, reveal the existence of informational correlations in finite-size thermodynamic systems.
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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 QTQ_TQT​, 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 QTQ_TQT​ 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 QTQ_TQT​ 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.
In conventional thermodynamics, a macroscopic process is characterized by changes in thermodynamic variables such as temperature, pressure, and entropy. In quantum thermodynamics, the state of a system is described by a density operator ρ, and the entropy of the system is given by the von Neumann entropy S = -k_B Tr(ρ ln ρ). Recent theoretical investigations have suggested that quantum coherence and phase correlations can also be thermodynamically relevant. This paper introduces the concept of Quantum Thermodynamic Phase Transfer (QTPT), a formalism that treats the quantum phase φ_T as a thermodynamic variable that can change during a process. We propose a set of postulates that extend the first and second laws of thermodynamics to include a term that accounts for the work associated with changes in φ_T. The framework is illustrated with a simple two–level system coupled to a thermal bath and driven by a time–dependent phase. We derive expressions for the generalized free energy and the entropy production that include phase contributions. The implications of QTPT for quantum heat engines, quantum refrigeration, and the fundamental limits of quantum thermodynamic cycles are discussed. The potential for a Nobel–level recognition of the unification of quantum coherence with classical thermodynamic principles is highlighted.
Thermometry in quantum mechanics has traditionally been anchored to the statistics of energy distributions, encapsulated by the Boltzmann factor where the probability of occupying an energy state E is proportional to exp(-E / (k_B T_E)). While effective in near-equilibrium regimes, this energy-centric paradigm falls short in strongly correlated systems, topological phases, and nonequilibrium steady states where energy fluctuations alone fail to capture the complete thermodynamic state. In this paper, we introduce Quantum Phase Thermometry Beyond Energy (QPTE), establishing an independent thermodynamic variable known as phase temperature, denoted as T_phi. Defined through the quantum phase fluctuations and the expectation value of the squared phase velocity operator as T_phi = (hbar * <\dot{\phi}^2>) / k_B, this framework transcends conventional energy measurements. We present a rigorous theoretical foundation showing that quantum phase fluctuations define an effective thermal scale distinct from traditional energy temperature. We explore the profound physical implications of the thermal discrepancy where T_phi not equal to T_E, demonstrating how QPTE expands the conceptual boundaries of statistical mechanics and fundamental thermodynamics.