A generalized theory of interactions for complex multiscale stochastic systems with thermodynamic irreversibility

Understanding nonlinear, hierarchically structured complex systems through the discovery and application of statistical mechanics principles remains a significant challenge. Considering thermodynamic irreversibility is simultaneously essential and often intractable in these cases. Additionally, the presence and filtering of noise across scales often translates into stochastic differential equations for the dynamics, a theoretically and computationally onerous task. We present ongoing work towards a novel mathematical physics development that aims to capture statistical mechanical properties of complex multiscale stochastic systems driven by irreversible thermodynamics, a generalized theory of interactions (GToI) with a purely relational view in which interactions are fundamental entities, while objects and laws are derived. We show how these can be instantiated into concrete theories of interaction (CToIs) capable of capturing key ensemble properties. We exemplify its application to unveiling the underlying complexity of gases and discuss some aspects of its relation to differential models, including relevant computational considerations.