Quantum Phase Thermometry Beyond Energy: A Framework for Independent Phase Temperature

Jincheng Zhang

Published Aug 11, 2026• 0 citations

Abstract

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.

DOI: 10.5281/zenodo.21888550

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