Coherent quantum oscillators are basic physical systems both in quantum statistical physics and quantum thermodynamics. Their realizations in lab often involve solid-state devices sensitive to changes in ambient temperature. We represent states of the solid-state optomechanical oscillator with temperature-dependent frequency by equivalent states of the mechanical oscillator with temperature-dependent energy levels. We interpret the temperature dependence as a consequence of strong coupling between the oscillator and the heat bath. We explore parameter regimes corresponding to anomalous behavior of mechanical and thermodynamic characteristics as a consequence of the strong coupling: (i) The localization and the purification induced by heating, and (ii) the negativity of two generalized heat capacities. The capacities can be used to witness non-linearity in the temperature dependency of the energy levels. Our phenomenological experimentally-oriented approach can stimulate development of new optomechanical and thermomechanical experiments exploring basic concepts of strong coupling thermodynamics.

Centro de Física Teórica e Computacional Departamento de Física Faculdade de Ciências Universidade de Lisboa Campo Grande P 1749 016 Lisboa Portugal

Charles University Faculty of Mathematics and Physics Department of Macromolecular Physics 5 Holešovičkách 2 180 00 Praha Czech Republic

Palacký University Department of Optics 17 listopadu 1192 12 771 46 Olomouc Czech Republic

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High-precision multiparameter estimation of mechanical force by quantum optomechanics