Conditional entropy and predictability for non-reversible Markov systems

The purpose of this thesis is to clarify the role of non-equilibrium stationary currents of Markov processes in the context of the predictability of future states of the system. Once the connection between the predictability and the conditional entropy is established, we provide a comprehensive approach to the definition of a multi-particle Markov system. In particular, starting from the well-known theory of random walk on network, we derive the non-linear master equation for an interacting multi-particle system under the one-step process hypothesis, highlighting the limits of its tractability and the prop- erties of its stationary solution. Lastly, in order to study the impact of the NESS on the predictability at short times, we analyze the conditional entropy by modulating the intensity of the stationary currents, both for a single-particle and a multi-particle Markov system. The results obtained analytically are numerically tested on a 5-node cycle network and put in correspondence with the stationary entropy production. Furthermore, because of the low dimensionality of the single-particle system, an analysis of its spectral properties as a function of the modulated stationary currents is performed.

Life Cycle Assessment comparativo tra il processo di co-digestione della frazione organica dei rifiuti solidi urbani e dei fanghi di depurazione disidratati e il sistema di gestione attuale. Il caso di Bagnacavallo (RA)

Waste management is becoming, year after year, always more important both for the costs associated with it and for the ever increasing volumes of waste generated. The discussion on the fate of organic fraction of municipal solid waste (OFMSW) leads everyday to new solutions. Many alternatives are proposed, ranging from incineration to composting passing through anaerobic digestion. “For Biogas” is a collaborative effort, between C.I.R.S.A. and R.E.S. cooperative, whose main goal is to generate “green” energy from both biowaste and sludge anaerobic co-digestion. Specifically, the project include a pilot plant receiving dewatered sludge from both urban and agro-industrial sewage (DS) and the organic fraction of MSW (in 2/1 ratio) which is digested in absence of oxygen to produce biogas and digestate. Biogas is piped to a co-generation system producing power and heat reused in the digestion process itself, making it independent from the national grid. Digestate undergoes a process of mechanical separation giving a liquid fraction, introduced in the treatment plant, and a solid fraction disposed in landfill (in future it will be further processed to obtain compost). This work analyzed and estimated the impacts generated by the pilot plant in its operative phase. Once the model was been characterized, on the basis of the CML2001 methodology, a comparison is made with the present scenario assumed for OFMSW and DS. Actual scenario treats separately the two fractions: the organic one is sent to a composting plant, while sludge is sent to landfill. Results show that the most significant difference between the two scenarios is in the GWP category as the project "For Biogas" is able to generate “zero emission” power and heat. It also generates a smaller volume of waste for disposal. In conclusion, the analysis evaluated the performance of two alternative methods of management of OFMSW and DS, highlighting that "For Biogas" project is to be preferred to the actual scenario.

Hidden Schrödinger symmetry in FLRW and Bianchi I minisuperspace models of cosmology and black holes Schwarzschild dynamics

A broad sector of literature focuses on the relationship between fluid dynamics and gravitational systems. This thesis presents results that suggest the existence of a new kind of fluid/gravity duality not based on the holographic principle. The goal is to provide tools that allow us to systematically unearth hidden symmetries for reduced models of cosmology. The focus is on the field space of these models, i.e. the superspace. In fact, conformal isometries of the supermetric leave geodesics in the field space unaltered; this leads to symmetries of the models. An innovative aspect is the use of the Eisenhart-Duval’s lift. Using this method, systems constrained by a potential can be treated as free ones. Moreover, charges explicitly dependent on time, i.e. dynamical, can be found. A detailed analysis is carried out on three basic models of homogenous cosmology: i) flat Friedmann-Lemaître-Robertson-Walker’s isotropic universe filled with a massless scalar field; ii) Schwarzschild’s black hole mechanics and its extension to vacuum (A)dS gravity; iii) Bianchi’s anisotropic type I universe with a massless scalar field. The results show the presence of a hidden Schrödinger’s symmetry which, being intrinsic to both Navier-Stokes’ and Schrödinger’s equations, indicates a correspondence between cosmology and hydrodynamics. Furthermore, the central extension of this algebra explicitly relates two concepts. The first is the number of particles coming from the fluid picture; while the second is the ratio between the IR and UV cutoffs that weighs how much a theory has of “classical” over “quantum”. This suggests a spacetime that emerges from an underlying world which is described by quantum building blocks. These quanta statistically conspire to appear as gravitational phenomena from a macroscopic point of view.