We study the abundance of a particle species in a thermalized plasma by introducing a quantum kinetic description based on the non-equilibrium effective action. A stochastic interpretation of quantum kinetics in terms of a Langevin equation emerges naturally. We consider a particle species that is stable in the vacuum and interacts with heavier particles that constitute a thermal bath in equilibrium. Asymptotic theory suggests a definition of a fully renormalized single particle distribution function. Its real time dynamics is completely determined by the non-equilibrium effective action which furnishes a Dyson-like resummation of the perturbative expansion. The distribution function reaches thermal equilibrium on a time scale ∼ 1/2 Γ k (T ) with Γ k (T ) being the quasiparticle relaxation rate. The equilibrium distribution function depends on the full spectral density as a consequence the fluctuation-dissipation relation. Such dependence leads to off-shell contributions to the particle abundance. A specific model of a bosonic field Φ in interaction with two heavier bosonic fields χ1,2 is studied. The decay of the heaviest particle and its recombination lead to a width of the spectral function for the particle Φ and to off-shell corrections to the abundance. We find substantial departures from the Bose-Einstein result both in the high temperature and the low temperature but high momentum region. In the latter the abundance is exponentially suppressed but larger than the Bose-Einstein result. We obtain the Boltzmann equation in renormalized perturbation theory and highlight the origin of the differences. Cosmological consequences are discussed: we argue that the corrections to the abundance of cold dark matter candidates are observationally negligible and that recombination erases any possible spectral distortions of the CMB. However we expect that the enhancement at high temperature may be important for baryogenesis.

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According to a standard view of the second law of thermodynamics, our belief in the second law can be justified by pointing out that low-entropy macrostates are less probable than high-entropy macrostates, and then noting that a system in an improbable state will tend to evolve toward a more probable state. I would like to argue that this justification of the second law is unhelpful at best and wrong at worst, and will argue that certain puzzles sometimes associated with the second law are merely artifacts of this questionable justification.

Although the canonical distribution is one of the central tools of statistical mechanics, the reason for its effectiveness is poorly understood. This is due in part to the fact that there is no clear consensus on what it means to use the canonical distribution to describe a system in equilibrium with a heat bath. I examine some traditional views as to what sort of thing we should take the canonical distribution to represent. I argue that a less explored alternative, according to which the canonical distribution represents a time ensemble of sorts, has a number of advantages that rival interpretations lack.

In a recent article in this journal, 1 Richard Gale and Alexander Pruss offer a new cosmological proof for the existence of God relying only on the Weak Principle of Sufficient Reason, W-PSR. We argue that their proof relies on applications of W-PSR that cannot be justified, and that our modal intuitions simply do not support W-PSR in the way Gale and Pruss take them to.