The first result of my Ph.D is an extension of the asymptotic fluctuation theorem (AFT) - a symmetry in the large deviation rate function of the time-averaged entropy production or heat dissipation of a process - from homogeneous stochastic processes to those driven by time-dependent protocols. A pre-print of the paper to appear in the Journal of Statistical Physics can be found here .
The second result is the derivation of a measure-theoretic identity underlying transient fluctuation theorems (TFTs), which generalize the second law of thermodynamics for systems observed at finite length and time-scales. The identity reveals a tautological interpretation of TFTs in terms of the arrow of time, sheds light on several recent results in the physics literature, and reveals an important reason why TFTs do not necessarily give rise to AFTs.
Some previous papers on agent-based modeling and dynamical systems done at Icosystem Corporation , the New England Complex Systems Institute and the Courant Institute at NYU