$$\mu PT$$ statistical ensemble: systems with fluctuating energy, particle number, and volume

Abstract

Within the theory of statistical ensemble, the so-called $$\mu PT$$ μ P T ensemble describes equilibrium systems that exchange energy, particles, and volume with the surrounding. General, model-independent features of volume and particle number statistics are derived. Non-analytic points of the partition function are discussed in connection with divergent fluctuations and ensemble equivalence. Quantum and classical ideal gases, and a model of Bose gas with mean-field interactions are discussed as examples of the above considerations.

Generalized uncertainty relation between thermodynamic variables in quantum thermodynamics

“…In this paper, we provide a general framework for calculating the uncertainty relation for each pair of thermodynamic intensive and extensive variables. Where we regarded the transition approach between different ensembles at the thermodynamic limit via a Legendre transformation [23][24][25][26]. We demonstrated that our results are consistent for all ensembles in any coupling regime.…”

“…In addition, one can redefine S from ln Z by a Legendre's transformation [23][24][25][26]. Let us consider an infinitesimal change d A i and dλ i of A i and λ i in equilibrium, respectively.…”

“…In the context of quantum-enhanced parameter estimation, the suitable measures to determine the ultimate limit of estimation precision is the Cramér-Rao (CR) bound [40][41][42] ∆θ ≥ 1 nF (θ) (26) with F (θ) being the quantum Fisher information and θ standing for the unknown parameter encoded in the initial state. As before, considering ρ = e G and G = − i λ i A i − ln Z, where λ i are the Lagrange coefficients, and A l |e j = a l |e j we can write the QFI in the following form [43][44][45]…”