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Contrary to the conventional wisdom that deviations from standardthermodynamics originate from the strong coupling to the bath, it is shown thatin quantum mechanics, these deviations originate from the uncertainty principleand are supported by the non-Markovian character of the dynamics. Specifically,it is shown that the lower bound of the dispersion of the total energy of thesystem, imposed by the uncertainty principle, is dominated by the bath powerspectrum and therefore, quantum mechanics inhibits the systemthermal-equilibrium-state from being described by the canonical Boltzmann'sdistribution. We show that for a wide class of systems, systems interacting viacentral forces with pairwise-self-interacting environments, this generalobservation is in sharp contrast to the classical case, for which the thermalequilibrium distribution, irrespective of the interaction strength, is\emph{exactly} characterized by the canonical Boltzmann distribution andtherefore, no dependence on the bath power spectrum is present. We define an\emph{effective coupling} to the environment that depends on all energy scalesin the system and reservoir interaction. Sample computations in regimespredicted by this effective coupling are demonstrated. For example, for thecase of strong effective coupling, deviations from standard thermodynamics arepresent and, for the case of weak effective coupling, quantum features such asstationary entanglement are possible at high temperatures.

Influence of Non-Markovian Dynamics in Thermal-Equilibrium Uncertainty-Relations