Linear and non-linear thermodynamics of a kinetic heat engine with fast transformations

We investigate a kinetic heat engine model constituted by particles enclosed in a box where one side acts as a thermostat and the opposite side is a piston exerting a given pressure. Pressure and temperature are varied in a cyclical protocol of period $\tau$ : their relative excursions, $\delta$ and $\epsilon$ respectively, constitute the thermodynamic forces dragging the system out-of-equilibrium. The analysis of the entropy production of the system allows to define the conjugated fluxes, which are proportional to the extracted work and the consumed heat. In the limit of small $\delta$ and $\epsilon$ the fluxes are linear in the forces through a $\tau$-dependent Onsager matrix whose off-diagonal elements satisfy a reciprocal relation. The dynamics of the piston can be approximated, through a coarse-graining procedure, by a Klein-Kramers equation which - in the linear regime - yields analytic expressions for the Onsager coefficients and the entropy production. A study of the efficiency at maximum power shows that the Curzon-Ahlborn formula is always an upper limit which is approached at increasing values of the thermodynamic forces, i.e. outside of the linear regime. In all our analysis the adiabatic limit $\tau \to \infty$ and the the small force limit $\delta,\epsilon \to 0$ are not directly related.Comment: 10 pages, 9 figure

A kinetic model for the finite-time thermodynamics of small heat engines

We study a molecular engine constituted by a gas of $N \sim 10^2$ molecules enclosed between a massive piston and a thermostat. The force acting on the piston and the temperature of the thermostat are cyclically changed with a finite period $\tau$. In the adiabatic limit $\tau \to \infty$, even for finite size $N$, the average work and heats reproduce the thermodynamic values, recovering the Carnot result for the efficiency. The system exhibits a stall time $\tau^*$ where net work is zero: for $\tau<\tau^*$ it consumes work instead of producing it, acting as a refrigerator or as a heat sink. At $\tau>\tau^*$ the efficiency at maximum power is close to the Curzorn-Ahlborn limit. The fluctuations of work and heat display approximatively a Gaussian behavior. Based upon kinetic theory, we develop a three-variables Langevin model where the piston's position and velocity are linearly coupled together with the internal energy of the gas. The model reproduces many of the system's features, such as the inversion of the work's sign, the efficiency at maximum power and the approximate shape of fluctuations. A further simplification in the model allows to compute analytically the average work, explaining its non-trivial dependence on $\tau$.Comment: 8 pages, 6 figures, accepted for publication on Physical Review

Fourier's Law in a Generalized Piston Model

A simplified, but non trivial, mechanical model -- gas of $N$ particles of mass $m$ in a box partitioned by $n$ mobile adiabatic walls of mass $M$ -- interacting with two thermal baths at different temperatures, is discussed in the framework of kinetic theory. Following an approach due to Smoluchowski, from an analysis of the collisions particles/walls, we derive the values of the main thermodynamic quantities for the stationary non-equilibrium states. The results are compared with extensive numerical simulations; in the limit of large $n$, $mN/M\gg 1$ and $m/M \ll 1$, we find a good approximation of Fourier's law.Comment: 14 pages, 5 figure

The role of the number of degrees of freedom and chaos in macroscopic irreversibility

This article aims at revisiting, with the aid of simple and neat numerical examples, some of the basic features of macroscopic irreversibility, and, thus, of the mechanical foundation of the second principle of thermodynamics as drawn by Boltzmann. Emphasis will be put on the fact that, in systems characterized by a very large number of degrees of freedom, irreversibility is already manifest at a single-trajectory level for the vast majority of the far-from-equilibrium initial conditions - a property often referred to as typicality. We also discuss the importance of the interaction among the microscopic constituents of the system and the irrelevance of chaos to irreversibility, showing that the same irreversible behaviours can be observed both in chaotic and non-chaotic systems.Comment: 21 pages, 6 figures, accepted for publication in Physica

Statistical mechanics and thermodynamics of small systems

In this thesis many aspects of the statistical mechanics and thermodynamics of small systems are studied. The very same possibility of defining a thermodynamics for this class of systems, for which the usual properties of the thermodynamic limit do not apply, is discussed by means of general considerations and specific examples. We show that it is possible to preserve most of the features of thermodynamics for a specific class of systems which are, at the same time, far enough from the infinite-N limit to be small, but large enough to be studied with a statistical approach. A review of the necessary mathematical and physical tools to study this particular class of systems is included. Eventually, a specific system is studied, both from an equilibrium and a non- equilibrium perspective: it is found that this system, composed by a gas included in a container with a moving wall (the piston), has an highly non-trivial dynamics caused by the interplay of the different degrees of freedom of the system, which cannot be easily reproduced by means of coarse-grained equations. At the same time, the smallness of the system is responsible for large fluctuations that strongly characterize the system. We show that this system reproduces the behavior of an heat engine, when the external parameters vary in time: in particular we show that different working regimes (engine, refrigerator, heat pump) can be obtained depending upon the total time of a cycle of the external parameters. We also derive some analytical results reproducing, with a fair degree of approximation, the behavior of the system

MDO applications to conventional and novel turboprop aircraft within agile European project

In this paper, multidisciplinary design optimization within the AGILE European project is applied to two turboprop aircraft. The first one is a conventional configuration characterized by wing mounted engines, while the second one is an innovative configuration with rear engines installation on the horizontal tail tip with an innovative power plant architecture. Both configurations are suited for 90 passengers, a design range of 1200 nautical miles and a cruise Mach number equal to 0.56. The methodologies used to analyze both configurations include aerodynamic performance in clean, landing and takeoff configurations, mission performance, weight and balance, stability and control, emissions, in terms of Global Warming Potential parameter, and Direct Operating Cost estimation. The latest two will be considered as objective functions for the optimization loop. Aim of this paper is to compare both configurations highlighting benefits and limits. Particular attention has been posed on the innovative approach used to analyze the use cases. The whole design process is made up ofdifferent tools belonging to a specific partner. Each partner is specialized in a specific discipline. The design process has been setup to be completely automated so that, partners, distributed worldwide are able to communicate and exchange results through remote connection. In this way each discipline has been assigned to the suited specialist

Environment and bladder cancer: molecular analysis by interaction networks

Bladder cancer (BC) is the 9th most common cancer worldwide, and the 6th most common cancer in men. Its development is linked to chronic inflammation, genetic susceptibility, smoking, occupational exposures and environmental pollutants. Aim of this work was to identify a sub-network of genes/proteins modulated by environmental or arsenic exposure in BC by computational network approaches. Our studies evidenced the presence of HUB nodes both in “BC and environment” and “BC and arsenicals” networks. These HUB nodes resulted to be correlated to circadian genes and targeted by some miRNAs already reported as involved in BC, thus suggesting how they play an important role in BC development due to environmental or arsenic exposure. Through data-mining analysis related to putative effect of the identified HUB nodes on survival we identified genes/proteins and their mutations on which it will be useful to focus further experimental studies related to the evaluation of their expression in biological matrices and to their utility as biomarkers of BC developmen

Streamlining Cross-Organizational Aircraft Development: Results from the AGILE Project

The research and innovation AGILE project developed the next generation of aircraft Multidisciplinary Design and Optimization processes, which target significant reductions in aircraft development costs and time to market, leading to more cost-effective and greener aircraft solutions. The high level objective is the reduction of the lead time of 40% with respect to the current state-of-the-art. 19 industry, research and academia partners from Europe, Canada and Russia developed solutions to cope with the challenges of collaborative design and optimization of complex products. In order to accelerate the deployment of large-scale, collaborative multidisciplinary design and optimization (MDO), a novel methodology, the so-called AGILE Paradigm, has been developed. Furthermore, the AGILE project has developed and released a set of open technologies enabling the implementation of the AGILE Paradigm approach. The collection of all the technologies constitutes AGILE Framework, which has been deployed for the design and the optimization of multiple aircraft configurations. This paper focuses on the application of the AGILE Paradigm on seven novel aircraft configurations, proving the achievement of the project’s objectives

A consistent description of fluctuations requires negative temperatures

We review two definitions of temperature in statistical mechanics, $T_B$ and $T_G$, corresponding to two possible definitions of entropy, $S_B$ and $S_G$, known as surface and volume entropy respectively. We restrict our attention to a class of systems with bounded energy and such that the second derivative of $S_B$ with respect to energy is always negative: the second request is quite natural and holds in systems of obvious relevance, i.e. with a number $N$ of degrees of freedom sufficiently large (examples are shown where $N \sim 100$ is sufficient) and without long-range interactions. We first discuss the basic role of $T_B$, even when negative, as the parameter describing fluctuations of observables in a sub-system. Then, we focus on how $T_B$ can be measured dynamically, i.e. averaging over a single long experimental trajectory. On the contrary, the same approach cannot be used in a generic system for $T_G$, since the equipartition theorem may be spoiled by boundary effects due to the limited energy. These general results are substantiated by the numerical study of a Hamiltonian model of interacting rotators with bounded kinetic energy. The numerical results confirm that the kind of configurational order realized in the regions at small $S_B$, or equivalently at small $|T_B|$, depends on the sign of $T_B$.Comment: 12 pages, 5 figures, accepted for publication in Journal of Statistical Mechanics: theory and experimen