Sven Schubert

Optimal Process Paths for Endoreversible Systems

Abstract All energy transformation processes occurring in reality are irreversible and in many cases these irreversibilities must be included in a realistic description of such processes. Endoreversible thermodynamics is a non-equilibrium approach in this direction by viewing a system as a network of internally reversible (endoreversible) subsystems exchanging energy in an irreversible fashion. All irreversibilities are confined to the interaction between the subsystems. This review is dedicated to the dynamical investigation of such endoreversible systems. First the general framework for the endoreversible description of a system is briefly introduced, and then the necessary mathematical tools to determine optimal process paths for such systems are presented. These are complemented by simple examples for the application of the different methods. Then the optimal paths for endoreversible processes of increasing complexity are discussed: first the processes between given equilibrium states, and then cyclic processes. These are followed by a review of internal combustion engines and by a number of further selected applications. We conclude with an outlook to other areas of irreversible thermodynamics where path optimization methods have been successfully used.

What Conditions Make Minimum Entropy Production Equivalent to Maximum Power Production

Optimization of processes can yield a variety of answers, depending not only on the objective of the optimization but also on the constraints that define the problem. Within the context of thermodynamic optimization, the role of the constraints is particularly important because, among other things, their choice can make some objectives either equivalent or inequivalent, and can limit or broaden the possible kinds of processes one might choose. After a general discussion of the principles, a specific example of a model power plant is analyzed to see how the constraints govern the possible solutions.

Coarse graining of a spin-glass state space

The complex structure of a spin-glass state space can be simplified by a coarse-graining procedure, i.e. microscopic states being assembled into larger clusters. An algorithm for the coarse graining of the state space of a short-range Ising spin glass is provided, which is the basis of a coarse-grained dynamics. Different ways for modelling the transition rates in the coarse-grained state space are discussed. A comparison with the dynamics of the microscopic system shows that the dynamics in the coarse-grained state space gives an appropriate approximation.

The state space of short-range Ising spin glasses: the density of states

The state space of finite square and cubic Ising spin glass models is analysed in terms of the global and the local density of states. Systems with uniform and gaussian probability distribution of interactions are compared. Different measures for the local state density are presented and discussed. In particular the question whether the local density of states grows exponentially or not is considered. The direct comparison of global and local densities leads to consequences for the structure of the state space.

The structure of enumerated spin glass state spaces

We enumerate the low energy part of the state space of an Ising spin glass using an efficient branch-and-bound algorithm. A coarse graining algorithm (NB-clustering) is employed to condense the inherent information to a system size which is treatable in computer simulations. The reduced state space still incorporates all ingredients necessary to simulate aging effects. We investigate its structure in detail and find that certain assumptions made in heuristical state space models which have been presented in the past to reproduce aging phenomena in spin glass experiments are indeed compatible with the data from the observed state spaces.

Preisach models of hysteresis driven by Markovian input processes

We study the response of Preisach models of hysteresis to stochastically fluctuating external fields. We perform numerical simulations, which indicate that analytical expressions derived previously for the autocorrelation functions and power spectral densities of the Preisach model with uncorrelated input, hold asymptotically also if the external field shows exponentially decaying correlations. As a consequence, the mechanisms causing long-term memory and 1/f noise in Preisach models with uncorrelated inputs still apply in the presence of fast decaying input correlations. We collect additional evidence for the importance of the effective Preisach density previously introduced even for Preisach models with correlated inputs. Additionally, we present some results for the output of the Preisach model with uncorrelated input using analytical methods. It is found, for instance, that in order to produce the same long-time tails in the output, the elementary hysteresis loops of large width need to have a higher weight for the generic Preisach model than for the symmetric Preisach model. Further, we find autocorrelation functions and power spectral densities to be monotonically decreasing independently of the choice of input and Preisach density.