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In two prior papers of this series, it was proposed that a wavefunction model of a heavy particle and a collection of light particles might generate ``Brownian-Motion-Like" trajectories as well as diffusive motion (displacement proportional to the square-root of time) of the heavy particle, but did not exhibit a concrete instance. Here we introduce a one-space-dimensional model which, granted a finite perturbation series, fulfills the criteria for BML trajectories and diffusion. We note that Planck's constant makes an appearance in the diffusion coefficient, which further differentiates the present theory from the work of Poincare and Einstein in the previous century.

In the first paper of this series, I investigated whether a wavefunction model of a heavy particle and a collection of light particles might generate "Brownian-Motion-Like" trajectories of the heavy particle. I concluded that it was possible, but left unsettled the second claim in Einstein's classical program: diffusive motion, proportional to the square-root of time, as opposed to ballistic motion, proportional to the time. In this paper, I derive a criterion for diffusive motion, as well as an expression for the diffusion coefficient. Unfortunately, as in paper I, no exact solutions are available for the models, making checking the criterion difficult. But a virtue of the method employed here is that, given adequate information about model eigenvalues and eigenfunctions, diffusion can be definitively ruled in or out.

Einstein's 1905 analysis of the Brownian Motion of a pollen grain in a water droplet as due to statistical variations in the collisions of water molecules with the grain, followed up by Perrin's experiments, provided one of the most convincing demonstrations of the reality of atoms. But in 1926 Schroedinger replaced classical particles by wavefunctions, which cannot undergo collisions. Can a Schroedingerist wavefunction physics account for Perrin's observations? As systems confined to a finite box can only generate quasiperiodic signals, this seems impossible, but I argue here that the issue is more subtle. I then introduce several models of the droplet-plus-grain; unfortunately, no explicit solutions are available (related is the remarkable fact that the harmonics of a general right triangle are still unknown). But from generic features of the models I conclude that: (a) wavefunction models may generate trajectories resembling those of a stochastic process; (b) diffusive behavior may appear for a restricted time interval; and (c) additional ``Wave Function Energy", by restricting ``cat" formation, can render the observations more ``classical". But completing the Einstein program of linking diffusion to viscosity and temperature in wavefunction models is still challenging.

From the point of view of Schr\"odingerism, a wavefunction-only philosophy, thermodynamics must be recast in terms of an ensemble of wavefunctions, rather than classical particle configurations or "found" values of Copenaghen Quantum Mechanics. Recapitulating the historical sequence, we consider here several models of magnets that classically can exhibit a phase transition to a low-temperature magnetized state. We formulate wavefunction analogues including a "Schr\"odingerist QUantum Ising Model" (SQUIM), a "Schr\"odingerist Curie-Weiss Model"(SCWM), and others. We show that the SQUIM with free boundary conditions and distinguishable "spins" has no finite-temperature phase transition, which we attribute to entropy swamping energy. The SCWM likewise, even assuming exchange symmetry in the wavefunction (in this case the analytical argument is not totally satisfactory and we helped ourself with a computer analysis). But a variant model with "Wavefunction Energy" (introduced in prior communications about Schr\"odingerism and the Measurement Problem) does have a phase transition to a magnetised state. The three results together suggest that magnetization in large wavefunction spin chains appears if and only if we consider indistinguishable particles and block macroscopic dispersion (i.e. macroscopic superpositions) by energy conservation. Our principle technique involves transforming the problem to one in probability theory, then applying results from Large Deviations, particularly the G\"artner-Ellis Theorem. Finally, we discuss Gibbs vs. Boltzmann/Einstein entropy in the choice of the quantum thermodynamic ensemble, as well as open problems. PhySH: quantum theory, quantum statistical mechanics, large deviation & rare event statistics. https://github.com/leodecarlo/Computing-Large-Deviation-Functionals-of-not-identically-distributed-independent-random-variables, Comment: A correction related to the ellipse figure, some conceptual comments and improvements in the proof of Theorem Two are added with respect to previous versions. In the journal version, first line after (15) page 5: "...and the O_i's are self-adjoint operators diagonal in the same base as H_{QM}" should be "...and the O_i's are self-adjoint operators such that (sum_i O_i)^2 is self-adjoint too"

In previous papers I expounded non-linear Schrodingerist quantum mechanics as a solution of the Measurement Problem. Here I show that NLQM is compatible with Einstein's theory of General Relativity. The extension to curved space-times presumes adoption of "space-time wavefunctions" (sometimes called "multi-time wavefunctions") and some additional algebraic structure: a "bitensor" supplementing Einstein's metric tensor. This kind of matter may violate the Strong Energy Condition even without a mass term, possibly with implications for the formation of singularities within Black Holes.

I discuss three proposed experiments that could in principle locate the boundary between the classical and quantum worlds, as well as distinguish the Hamiltonian theory presented in the first paper of this series from the spontaneous-collapse theories.

Paper I of this series introduced a nonlinear version of quantum mechanics that blocks cats, and paper II postulated a random part of the wavefunction to explain outcomes in experiments such as Stern-Gerlach or EPRB. However, an ad hoc extra parameter was assumed for the randomness. Here I provide some analytic and simulation evidence that the nonlinear theory exhibits sensitive dependence on initial conditions in measurement scenarios, perhaps implying that the magnitude of randomness required is determined by structural features of the model, and does not require a free parameter.

In the first paper of this series, I introduced a non-linear, Hamiltonian, generalization of Schroedinger's theory that blocks formation of macroscopic dispersion ("cats"). But that theory was entirely deterministic, and so the origin of random outcomes in experiments such as Stern-Gerlach or EPRB was left open. Here I propose that Schroedinger's wavefunction has a random component and demonstrate that such an improvised stochastic theory can violate Bell's inequality. Repeated measurements and the back-reaction on the microsystem are discussed in a toy example. Experiments that might falsify the theory are described.

Working entirely within the Schroedinger paradigm, meaning wavefunction only, I present a modification of his theory that prevents formation of macroscopic dispersion (MD; "cats"). The proposal is to modify the Hamiltonian based on a method introduced by Steven Weinberg in 1989, as part of a program to test quantum mechanics at the atomic or nuclear level. By contrast, the intent here is to eliminate MD without affecting the predictions of quantum mechanics at the microscopic scale. This restores classical physics at the macro level. Possible experimental tests are indicated and the differences from previous theories discussed. In a second paper, I will address the other difficulty of wavefunction physics without the statistical (Copenhagen) interpretation: how to explain random outcomes in experiments such as Stern-Gerlach, and whether a Schroedingerist theory with a random component can violate Bell's inequality.

In two previous papers, I introduced SuperSpreader (SS) epidemic models, offered some theoretical discussion of prevention issues, and fitted some models to data derived from published accounts of the ongoing MERS epidemic (concluding that a pandemic is likely). Continuing on this theme, here I discuss prediction: whether, in a disease outbreak driven by superspreader events, a rigorous decision point---meaning a declaration that a pandemic is imminent---can be defined. I show that all sources of prediction bias contribute to generating false negatives (i.e., discounting the chance of a pandemic when it is looming or has already started). Nevertheless, the statistical difficulties can be overcome by improved data gathering and use of known techniques that decrease bias. One peculiarity of the SS epidemic is that the prediction can sometimes be made long before the actual pandemic onset, generating lead time to alert the medical community and the public. Thus modeling is useful to overcome a false sense of security arising from the long "kindling times" characteristic of SS epidemics and certain political/psychological factors, as well as improve the public health response.

In a paper of August 2013, I discussed the so-called SuperSpreader (SS) epidemic model and emphasized that it has dynamics differing greatly from the more-familiar uniform (or Poisson) textbook model. In that paper, SARS in 2003 was the representative instance and it was suggested that MERS may be another. In April 2014, MERS incident cases showed a spectacular spike (going from a handful in the previous April to more than 260 in that month of 2014) reminiscent of a figure I published nine months earlier. Here I refit the two-level and several variant SS models to incident data from January 1, 2013--April 30, 2014 and conclude that MERS will go pandemic (all other factors remaining the same). In addition, I discuss a number of model-realism and fitting methodology issues relevant to analysing SS epidemics.

I discuss the so-called SuperSpreader epidemic, for which SARS is the canonical examples (and, perhaps, MERS will be another). I use simulation by an agent-based model as well as the mathematics of multi-type branching-processes to illustrate how the SS epidemic differs from the more familiar uniform epidemic (e.g., caused by influenza). The conclusions may surprise the reader: (a) The SS epidemic must be described by at least two numbers, such as the mean reproductive number (of "secondary" cases caused by a "primary case"), R0, and the variance of same, call it V0; (b) Even if R0 > 1, if V0 >> R0 the probability that an infection-chain caused by one primary case goes extinct without intervention may be close to one (e.g., 0.97); (c) The SS epidemic may have a long "kindling period" in which sporadic cases appear (transmitted from some unknown host) and generate a cluster of cases, but the chains peter out, perhaps generating a false sense of security that a pandemic will not occur; (d) Interventions such as isolation (or contact-tracing and secondary case isolation) may prove efficacious even without driving R0 below one; (e) The efficacy of such interventions diminishes, but slowly, with increasing V0 at fixed R0. From these considerations, I argue that the SS epidemic has dynamics sufficiently distinct from the uniform case that efficacious public-health interventions can be designed even in the absence of a vaccine or other form of treatment.