Ever since Einstein’s description of Brownian motion, the mathematics of Markovian stochastic processes proved a crucial paradigm for the understanding of the behaviour of open systems interacting with a large (and thus memory-less) environment. When such processes occur on an intrinsically discrete configuration space, the topology of the network of possible transitions furnishes important insights about the nature of nonequilibrium processes. In this talk I will 1) trace the conceptual path that leads from the abstraction of open systems to the mathematics of Markov processes on networks, 2) mention some of the major findings that are novel with respect to textbook thermodynamics, 3) outline some recent developments regarding the role of an ideal observer who only has partial information about the system.
Effective thermodynamics for a marginal observer
Thermodynamic modeling often presumes that the observer has complete information about the system she or he deals with: no parasitic current, exact evaluation of the forces needed to drive the system out of equilibrium. However, most often the observer only measures marginal information. How is she or he to make consistent thermodynamic claims? Disregarding sources of dissipation might lead to untenable claims, such as the possibility of perpetuum mobile. Basing on the tenets of Stochastic Thermodynamics, we show that for such an observer it is nevertheless possible to produce an effective description that does not dispense with the fundamentals of thermodynamics: the 2nd Law, the Fluctuation-Dissipation paradigm, and the more recent and encompassing Fluctuation Theorem.