# Time–Energy and Time–Entropy Uncertainty Relations in Nonequilibrium Quantum Thermodynamics under Steepest-Entropy-Ascent Nonlinear Master Equations

@article{Beretta2019TimeEnergyAT,
title={Time–Energy and Time–Entropy Uncertainty Relations in Nonequilibrium Quantum Thermodynamics under Steepest-Entropy-Ascent Nonlinear Master Equations},
author={Gian Paolo Beretta},
journal={Entropy},
year={2019},
volume={21}
}
In the domain of nondissipative unitary Hamiltonian dynamics, the well-known Mandelstam–Tamm–Messiah time–energy uncertainty relation τFΔH≥ℏ/2 provides a general lower bound to the characteristic time τF=ΔF/|d〈F〉/dt| with which the mean value of a generic quantum observable F can change with respect to the width ΔF of its uncertainty distribution (square root of F fluctuations). A useful practical consequence is that in unitary dynamics the states with longer lifetimes are those with smaller…
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## References

SHOWING 1-10 OF 151 REFERENCES

• G. Beretta
• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2006
We discuss a nonlinear model for relaxation by energy redistribution within an isolated, closed system composed of noninteracting identical particles with energy levels with . The time-dependent
• Physics
• 2013
We present a family of steepest entropy ascent (SEA) models of the Boltzmann equation. The models preserve the usual collision invariants (mass, momentum, energy), as well as the non-negativity of
• Physics
• 1995
A precise form of the quantum-mechanical time-energy uncertainty relation is derived. For any given initial state (density operator), time-dependent Hamiltonian, and subspace of reference states, it
We derive a well-behaved nonlinear extension of the non-relativistic Liouville-von Neumann dynamics driven by maximal entropy production with conservation of energy and probability. The pure state
• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2015
The steepest-entropy-ascent dynamical model for nonequilibrium thermodynamics in the mathematical language of differential geometry is reformulated and a formal proof that in more general frameworks, the SEA and GENERIC models of the dissipative component of the dynamics are essentially interchangeable, provided of course they assume the same kinematics.
In the framework of the recent quest for well-behaved nonlinear extensions of the traditional Schrodinger-von Neumann unitary dynamics that could provide fundamental explanations of recent
• G. Beretta
• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2014
It is hoped that the present unifying approach may prove useful in providing a fresh basis for effective, thermodynamically consistent, numerical models and theoretical treatments of irreversible conservative relaxation towards equilibrium from far nonequilibrium states.
• Physics
Physical review. A, Atomic, molecular, and optical physics
• 1994
A new derivation from first principle is given of the energy-time uncertainty relation in quantum mechanics, and a canonical transformation is made in clusical mechanic that creates a new canonical coordinate T, which is called tempu, co~ugate to the energy.