Stochastic Thermodynamics and Information Processing

An accumulation of experimental evidence over the past two decades has tightened the relationship between thermodynamics and the emergence of structure in driven natural systems. A plausible explanation for how structure emerges has arisen from the theory of stochastic thermodynamics called dissipative adaptation. As thermodynamic systems transition between states due to thermal fluctuations and external agency, the system is biased towards states that efficiently absorb energy from the applied force. The theory shows promise in explaining many challenging concepts such as phase transitions and evolutionary adaptation. However, nature is replete with systems that augment their configuration and act on their environment with apparent intent. In its current formulation, dissipative adaptation offers no insight into the mechanisms underlying this emergent feedback behavior. In this work, we propose that by integrating recent advances in stochastic process research and information theory we can extend this first principles approach to study the emergence of information processing. We propose a novel probabilistic graphical model that captures the underlying principles of stochastic thermodynamic systems capable of measurement. The model is based on an emerging discipline that integrates information into stochastic thermodynamics known as thermodynamics of information. Modern work in stochastic optimization theory provides a provably convergent stochastic approximation algorithm based on the Robbins-Munro algorithm that follows from the extended second law of thermodynamics. Finally, we will examine loosely coupled networks of individual systems that obey our stochastic optimization scheme while being stimulated by a transient data generating distribution and observe the hypothesized emergent behavior.