Local kinetic interpretation of entropy production through reversed diffusion.

The time reversal of stochastic diffusion processes is revisited with emphasis on the physical meaning of the time-reversed drift and the noise prescription in the case of multiplicative noise. The local kinematics and mechanics of free diffusion are linked to the hydrodynamic description. These properties also provide an interpretation of the Pope-Ching formula for the steady-state probability density function along with a geometric interpretation of the fluctuation-dissipation relation. Finally, the statistics of the local entropy production rate of diffusion are discussed in the light of local diffusion properties, and a stochastic differential equation for entropy production is obtained using the Girsanov theorem for reversed diffusion. The results are illustrated for the Ornstein-Uhlenbeck process.

Latent Space and Social Psychological Models of Diffusion

The problem of social diffusion has animated sociological thinking on topics ranging from the spread of an idea, an innovation or a disease, to the foundations of collective behavior and political polarization. While network diffusion has been a productive metaphor, the reality of diffusion processes is often muddier. Ideas and innovations diffuse differently from diseases, but, with a few exceptions, the diffusion of ideas and innovations has been modeled under the same assumptions as the diffusion of disease. In this dissertation, I develop two new diffusion models for "socially meaningful" contagions that address two of the most significant problems with current diffusion models: (1) that contagions can only spread along observed ties, and (2) that contagions do not change as they spread between people. I augment insights from these statistical and simulation models with an analysis of an empirical case of diffusion - the use of enterprise collaboration software in a large technology company. I focus the empirical study on when people abandon innovations, a crucial, and understudied aspect of the diffusion of innovations. Using timestamped posts, I analyze when people abandon software to a high degree of detail.

To address the first problem, I suggest a latent space diffusion model. Rather than treating ties as stable conduits for information, the latent space diffusion model treats ties as random draws from an underlying social space, and simulates diffusion over the social space. Theoretically, the social space model integrates both actor ties and attributes simultaneously in a single social plane, while incorporating schemas into diffusion processes gives an explicit form to the reciprocal influences that cognition and social environment have on each other. Practically, the latent space diffusion model produces statistically consistent diffusion estimates where using the network alone does not, and the diffusion with schemas model shows that introducing some cognitive processing into diffusion processes changes the rate and ultimate distribution of the spreading information. To address the second problem, I suggest a diffusion model with schemas. Rather than treating information as though it is spread without changes, the schema diffusion model allows people to modify information they receive to fit an underlying mental model of the information before they pass the information to others. Combining the latent space models with a schema notion for actors improves our models for social diffusion both theoretically and practically.

The empirical case study focuses on how the changing value of an innovation, introduced by the innovations' network externalities, influences when people abandon the innovation. In it, I find that people are least likely to abandon an innovation when other people in their neighborhood currently use the software as well. The effect is particularly pronounced for supervisors' current use and number of supervisory team members who currently use the software. This case study not only points to an important process in the diffusion of innovation, but also suggests a new approach -- computerized collaboration systems -- to collecting and analyzing data on organizational processes.