Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.

Life Cycle Assessment of Peach Nectar: a comparative analysis between conventional and bioenergy-from-waste integrated food chains

Modern food systems are characterized by a high energy intensity as well as by the production of large amounts of waste, residuals and food losses. This inefficiency presents major consequences, in terms of GHG emissions, waste disposal, and natural resource depletion. The research hypothesis is that residual biomass material could contribute to the energetic needs of food systems, if recovered as an integrated renewable energy source (RES), leading to a sensitive reduction of the impacts of food systems, primarily in terms of fossil fuel consumption and GHG emissions. In order to assess these effects, a comparative life cycle assessment (LCA) has been conducted to compare two different food systems: a fossil fuel-based system and an integrated system with the use of residual as RES for self-consumption. The food product under analysis has been the peach nectar, from cultivation to end-of-life. The aim of this LCA is twofold. On one hand, it allows an evaluation of the energy inefficiencies related to agro-food waste. On the other hand, it illustrates how the integration of bioenergy into food systems could effectively contribute to reduce this inefficiency. Data about inputs and waste generated has been collected mainly through literature review and databases. Energy balance, GHG emissions (Global Warming Potential) and waste generation have been analyzed in order to identify the relative requirements and contribution of the different segments. An evaluation of the energy “loss” through the different categories of waste allowed to provide details about the consequences associated with its management and/or disposal. Results should provide an insight of the impacts associated with inefficiencies within food systems. The comparison provides a measure of the potential reuse of wasted biomass and the amount of energy recoverable, that could represent a first step for the formulation of specific policies on the integration of bioenergies for self-consumption.

Markov Constraints for Generating Texts with Style

This thesis addresses the issue of generating texts in the style of an existing author, that also satisfy structural constraints imposed by the genre of the text. Although Markov processes are known to be suitable for representing style, they are difficult to control in order to satisfy non-local properties, such as structural constraints, that require long distance modeling. The framework of Constrained Markov Processes allows to precisely generate texts that are consistent with a corpus, while being controllable in terms of rhymes and meter. Controlled Markov processes consist in reformulating Markov processes in the context of constraint satisfaction. The thesis describes how to represent stylistic and structural properties in terms of constraints in this framework and how this approach can be used for the generation of lyrics in the style of 60 differents authors An evaluation of the desctibed method is provided by comparing it to both pure Markov and pure constraint-based approaches. Finally the thesis describes the implementation of an augmented text editor, called Perec. Perec is intended to improve creativity, by helping the user to write lyrics and poetry, exploiting the techniques presented so far.