Smooth Entropy in Axiomatic Thermodynamics

Thermodynamics can be formulated in either of two approaches, the phenomenological approach, which refers to the macroscopic properties of systems, and the statistical approach, which describes systems in terms of their microscopic constituents. We establish a connection between these two approaches by means of a new axiomatic framework that can take errors and imprecisions into account. This link extends to systems of arbitrary sizes including very small systems, for which the treatment of imprecisions is pertinent to any realistic situation. Based on this, we identify the quantities that characterise whether certain thermodynamic processes are possible with entropy measures from information theory. In the error-tolerant case, these entropies are so-called smooth min and max entropies. Our considerations further show that in an appropriate macroscopic limit there is a single entropy measure that characterises which state transformations are possible. In the case of many independent copies of a system (the so-called i.i.d. regime), the relevant quantity is the von Neumann entropy. Transformations among microcanonical states are characterised by the Boltzmann entropy

Exergy analysis of incremental sheet forming

Research in the last 15 years has led to die-less incremental forming processes that are close to realization in an industrial setup. Whereas many studies have been carried out with the intention of investigating technical abilities and economic consequences, the ecological impact of incremental sheet forming (ISF) has not been studied so far. Using the concept of exergy analysis, two ISF technologies, namely single sided and double sided incremental forming, are investigated and compared to conventional forming and hydroforming. A second exergy analysis is carried out with the purpose of examining the environmental impact of different forming technologies from a supply chain perspective. Therefore, related upstream activities (die set production, aluminum sheet production and energy conversion and supply) are included into the exergy analysis. The entire supply chain is modeled with Matlab/Simulink. The results of both analyses suggest that ISF is environmentally advantageous for prototyping and small production runs.United States. Dept. of Energy (Award DE-EE0003460

The entropy concept for non-equilibrium states

In earlier work, we presented a foundation for the second law of classical thermodynamics in terms of the entropy principle. More precisely, we provided an empirically accessible axiomatic derivation of an entropy function defined on all equilibrium states of all systems that has the appropriate additivity and scaling properties, and whose increase is a necessary and sufficient condition for an adiabatic process between two states to be possible. Here, after a brief review of this approach, we address the question of defining entropy for non-equilibrium states. Our conclusion is that it is generally not possible to find a unique entropy that has all relevant physical properties. We do show, however, that one can define two entropy functions, called S(−) and S(+), which, taken together, delimit the range of adiabatic processes that can occur between non-equilibrium states. The concept of comparability of states with respect to adiabatic changes plays an important role in our reasoning