We show, by making use of the functional integral technique, that, for a large class of useful quantum statistical systems, the partition function is, with respect to the coupling constant, the Laplace transform of a positive measure. As a consequence, we derive an infinite set of monotonicly converging upper and lower bounds to it. In particular, the lowest approximation appears to be identical to the Gibbs–Bogolioubov variational bound, while the next approximations, for which we give explicit formulas for the first few ones, lead to improve the previous bound. The monotonic character of the variational successive approximations allows a new approach towards the thermodynamical limit.

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Non-recurrent short term variations of the galactic cosmic-ray (GCR) flux above 70 MeV n −1 were observed between 2016 February 18 and 2017 July 3 aboard the European Space Agency LISA Pathfinder (LPF) mission orbiting around the Lagrange point L1 at 1.5×10 6 km from Earth. The energy dependence of three Forbush decreases (FDs) is studied and reported here. A comparison of these observations with others carried out in space down to the energy of a few tens of MeV n −1 shows that the same GCR flux parameterization applies to events of different intensity during the main phase. FD observations in L1 with LPF and geomagnetic storm occurrence is also presented.Finally, the characteristics of GCR flux non-recurrent variations (peaks and depressions) of duration < 2 days and their association with interplanetary structures are investigated. It is found that, most likely, plasma compression regions between subsequent corotating high-speed streams cause peaks, while heliospheric current sheet crossing cause the majority of the depressions.