Temperature--Hamiltonian Ambiguity in Strong-Coupling Quantum Equilibrium
Abstract
Strong coupling generally drives a subsystem away from the Gibbs state of its bare Hamiltonian at the bath temperature. We formulate a temperature--Hamiltonian ambiguity: the reduced equilibrium state fixes the dimensionless Gibbs generator, but does not by itself uniquely determine the local Hamiltonian and temperature entering a Gibbs representation. We propose an operational resolution in which the local Hamiltonian is identified from physical information independent of the stationary Gibbs parametrization. Whenever the exact reduced state is compatible with the Gibbs family generated by that independently identified Hamiltonian, it then determines a unique local temperature. An exactly solvable two-level-system--oscillator model makes the ambiguity explicit through state-equivalent descriptions based on temperature renormalization relative to a specified local Hamiltonian and Hamiltonian-of-mean-force level renormalization at the bath temperature. An exact bosonic model provides the complementary case in which retarded dynamics independently fixes a renormalized local excitation scale and thereby specifies the local Hamiltonian before the stationary populations determine the temperature. These results distinguish state representation from thermodynamic assignment and provide an operational framework for local thermodynamics beyond weak coupling.
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BibTeX
@misc{jin2026temperaturehamiltonian,
title = {{Temperature--Hamiltonian Ambiguity in Strong-Coupling Quantum Equilibrium}},
author = {Jinshuang Jin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33389},
eprint = {2609.33389},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33389},
}
RIS
TY - UNPB
TI - Temperature--Hamiltonian Ambiguity in Strong-Coupling Quantum Equilibrium
AU - Jinshuang Jin
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33389
UR - https://arxiv.org/abs/2609.33389
AB - Strong coupling generally drives a subsystem away from the Gibbs state of its bare Hamiltonian at the bath temperature. We formulate a temperature--Hamiltonian ambiguity: the reduced equilibrium state fixes the dimensionless Gibbs generator, but does not by itself uniquely determine the local Hamiltonian and temperature entering a Gibbs representation. We propose an operational resolution in which the local Hamiltonian is identified from physical information independent of the stationary Gibbs parametrization. Whenever the exact reduced state is compatible with the Gibbs family generated by that independently identified Hamiltonian, it then determines a unique local temperature. An exactly solvable two-level-system--oscillator model makes the ambiguity explicit through state-equivalent descriptions based on temperature renormalization relative to a specified local Hamiltonian and Hamiltonian-of-mean-force level renormalization at the bath temperature. An exact bosonic model provides the complementary case in which retarded dynamics independently fixes a renormalized local excitation scale and thereby specifies the local Hamiltonian before the stationary populations determine the temperature. These results distinguish state representation from thermodynamic assignment and provide an operational framework for local thermodynamics beyond weak coupling.
ER -