Generalized uncertainty relation between thermodynamic variables in quantum thermodynamics

Abstract

Macroscopic thermodynamics, via the weak coupling approximation, assumes that the equi?librium properties of a system are not affected by interactions with its environment. However, this assumption may not hold for quantum systems, where the strength of interaction between the system and the environment may become non-negligible in a strong coupling regime. In such a regime, the equilibrium properties of the system depend on the interaction energy and the system state is no longer of the Gibbs form. Regarding such interactions, using tools from the quantum estimation theory, we derive the thermodynamic uncertainty relation between intensive and exten?sive variables valid at all coupling regimes through the generalized Gibbs ensemble (GGE). Where we demonstrate the lower bound on the uncertainty of intensive variables increases in presence of quantum fluctuations. Also, we calculate the general uncertainty relations for several ensembles to corroborate the literature results, thus showing the versatility of our method.

arXiv comment23 pages

References in corpus (25)

• Advances in Quantum Metrology
• Quantum Fisher information matrix and multiparameter estimation
• Generalized Gibbs ensemble in integrable lattice models
• Characterizing Nonclassical Correlations via Local Quantum Uncertainty
• Quantum speed limits, coherence and asymmetry
• First and Second Law of Thermodynamics at strong coupling
• Quantum Fisher information for states in exponential form
• Making Sense of the Legendre Transform
• Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges
• Monogamy of quantum correlations - a review
• Stochastic thermodynamics in the strong coupling regime: An unambiguous approach based on coarse-graining
• The equilibrium states of open quantum systems in the strong coupling regime
• Entropy production and time-asymmetry in the presence of strong interactions
• Bridging thermodynamics and metrology in non-equilibrium Quantum Thermometry
• Maximal Quantum Fisher Information for Mixed States
• Skew informations from an operational view via resource theory of asymmetry
• Noncommuting conserved quantities in quantum many-body thermalization
• Quantum variance: a measure of quantum coherence and quantum correlations for many-body systems
• Hamiltonian of mean force for damped quantum systems
• Thermal energies of classical and quantum damped oscillators coupled to reservoirs
• Measuring effective temperatures in a generalized Gibbs ensemble
• The thermodynamic entropy of a macroscopic quantum system is a continuous function of energy
• Noncommutative generalized Gibbs ensemble in isolated integrable quantum systems
• Relating relative Rényi entropies and Wigner-Yanase-Dyson skew information to generalized multiple quantum coherences
• $\mu PT$ statistical ensemble: systems with fluctuating energy, particle number, and volume