- We study the inflationary quantum-to-classical transition for the adiabatic curvature perturbation due to quantum decoherence, focusing on the role played by squeezed-limit mode couplings. We evolve the quantum state in the Schrodinger picture, for a generic cubic coupling to additional environment degrees of freedom. Focusing on the case of minimal gravitational interactions, we find the evolution of the reduced density matrix for a given long-wavelength fluctuation by tracing out the other (mostly shorter wavelength) modes of as an environment. We show that inflation produces phase oscillations in the wave functional , which suppress off-diagonal components of the reduced density matrix, leaving a diagonal mixture of different classical configurations. Gravitational nonlinearities thus provide a minimal mechanism for generating classical stochastic perturbations from inflation. We identify the time when decoherence occurs, which is delayed after horizon crossing due to the weak coupling, and find that Hubble-scale modes act as the decohering environment. We also comment on the observational relevance of decoherence and its relation to the squeezing of the quantum state.
**Nonequilibrium fluctuation-dissipation inequality and nonequilibrium uncertainty principle**

*C. H. Fleming, B. L. Hu, Albert Roura*The*fluctuation-dissipation relation*is usually formulated for a system interacting with a heat bath at finite temperature, and often in the context of linear response theory, where only small deviations from the mean are considered. We show that for an open quantum system interacting with a nonequilibrium environment, where temperature is no longer a valid notion, a*fluctuation-dissipation inequality*exists. Instead of being proportional, quantum fluctuations are bounded below by quantum dissipation, whereas classically the fluctuations vanish at zero temperature. The lower bound of this inequality is exactly satisfied by (zero-temperature) quantum noise and is in accord with the Heisenberg uncertainty principle, in both its microscopic origins and its influence upon systems.

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