Reconstructing thermodynamics from quantum Fisher information

Angelo Plastino, F. Pennini

Austin K. Daniel, Yuri V. Rostovtsev

Nadal Vidal Jose Israel

The coherent ergotropy of a quantum system—the work extractable by unitary control that is stored in energy-basis coherences—is usually treated as a purely thermodynamic quantity. This preprint establishes its exact geometric content for a two-level system and precisely delineates the limits of that connection. First, it proves the exact identity C = ε(√(z² + F_Q) − |z|), where z is the population imbalance and F_Q is the quantum Fisher information conjugate to the level phase, equivalently the squared Ramsey visibility. Coherent work is therefore a joint function of the population imbalance and the phase QFI, rather than a function of the QFI alone. Second, an exact two-level bound C ≤ ½√(F_Q^H) is established for the Hamiltonian-generated quantum Fisher information, with saturation on the Bloch equator. An explicit qutrit counterexample, extended by embedding, demonstrates that this bound fails for every dimension d ≥ 3. The work further corrects the target state entering the quantum speed-limit formulation of work extraction, showing that unitary extraction must drive the system toward its passive state rather than its dephased state. Finally, the exact identity predicts an anisotropic coherence horizon under pure dephasing: the 1/e lifetime of coherent work changes continuously from T2 on the Bloch equator to T2/2 near the poles. Coherent ergotropy can consequently be reconstructed experimentally from three calibrated quantities—the population imbalance, Ramsey visibility, and level splitting—without a work-extraction protocol, full state tomography, or an ancilla.

Sebastian Deffner, Steve Campbell

Darren Campbell, Darren Campbell

Description:A reconstruction theory for complex quantum coherence encoded on graphs using controlled quantum Fisher information. Finite-order data determine edge magnitudes and cycle holonomies up to an explicit integral-lattice ambiguity, revealing continuous and torsion obstructions to identifiability. With physical labelled Schur controls, exact finite-value measurements reconstruct the full coherence matrix up to vertex gauge using at most |E| + 2β scalar QFI values, with explicit injectivity and stability bounds. .

Laetitia P. Bettmann, John Goold

Recent advancements have revealed new links between information geometry and classical stochastic thermodynamics, particularly through the Fisher information (FI) with respect to time. Recognizing the nonuniqueness of the quantum Fisher metric in Hilbert space, we exploit the fact that any quantum Fisher information (QFI) can be decomposed into a metric-independent incoherent part and a metric-dependent coherent contribution. We demonstrate that the incoherent component of any QFI can be directly linked to entropic acceleration, and for GKSL dynamics with local detailed balance, to the rate of change of generalized thermodynamic forces and entropic flow, paralleling the classical results. Furthermore, we tighten a classical uncertainty relation between the geometric uncertainty of a path in state space and the time-averaged rate of information change and demonstrate that it also holds for quantum systems. We generalize a classical geometric bound on the entropy rate for far-from-equilibrium processes by incorporating a nonnegative quantum contribution that arises from the geometric action due to coherent dynamics. Finally, we apply an information-geometric analysis to the recently proposed quantum-thermodynamic Mpemba effect, demonstrating this framework's ability to capture thermodynamic phenomena.