Peter Salamon

Thermodynamics in finite time: extremals for imperfect heat engines

A general description is developed for processes involving work and two heat reservoirs or three heat reservoirs in terms of rates for continuous processes or of cycle averages for periodic processes. The description is applied to heat engines having friction, thermal resistance, and heat losses in order to determine the maximum power and maximum efficiency of such engines. By use of a geometric representation the reversible and irreversible parts of a process are separated as the components of a vector. This leads to the definition of a dimensionless quantity that measures irreversibility and is related in a complementary way to the traditional concept of efficiency. The new quantity appears to be useful in cases where efficiency has no well‐defined meaning.

On a relation between economic and thermodynamic optima

Abstract We present necessary and sufficient conditions that a least-cost production system operates within e of its thermodynamic limit. The theorem can be extended, with the knowledge of the production function, to fix the economically-efficient level of thermodynamic efficiency or effectiveness. The analysis is also extended to cases in which several factors of production have different thermodynamic limits. The theorems, while weak, appear to represent the first precise relationship between economic and thermodynamic extrema.

The optimal simulated annealing schedule for a simple model

Used as a tool for large scale global optimisation, simulated annealing incurs heavy computational costs. Therefore, choosing an optimal cooling schedule is of great scientific and economic importance. For the first time an analytic as well as a numeric solution to this problem is presented, albeit only for a small example system. The example shows the role of optimal control theory for this problem.

Stochastic dynamics of supervised learning

The stochastic evolution of adiabatic (slow) backpropagation training of a neural network is discussed and a Fokker-Planck equation for the post-training distribution function in the network space is derived. The distribution obtained differs from the one given by Radons et al. (1990). Studying the character of the post-training distribution, the authors find that, except under very special circumstances, the distribution will be non-Gibbsian. The validity of the present approach is tested on a simple backpropagation learning system in one dimension, which can be solved analytically as well. Implications of the Fokker-Planck approach for general situations are examined in the local linear approximation. Surprisingly they find that the post-training distribution is isotropic close to its peak, hence simpler than the corresponding Gibbs distribution.

Simulated annealing for single minimum optimization problems

Two examples are presented which show that simulated annealing can perform better than quenching and steepest descent even on problems with a single minimum. An implication for real global optimization problems is that simulated annealing can be useful even on time scales which are short compared to the time required for a greedy algorithm to reach the nearest local minimum.