The class of thermodynamic processes with given rate and minimal entropy production is considered. The general conditions they obey are derived. It is shown how the application of those conditions to a number of particular systems produces a number of known bounds on entropy production ͑for heat and mass transfer processes and chemical conversion͒ as well as previously unknown bounds ͑for throttling, crystallization, and mechanical friction͒. ͓S1063-651X͑98͒04307-4͔

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The criterion of thermodynamic ideality is introduced. It is the ratio of actual rate of entropy production to the minimal rate of entropy production. It is closely related to the exergy approach but incorporates the irreversible losses due to finite-time and nonzero rates. No explicit reference need be made to the average values of the thermodynamic potentials of the environment. The regimes with minimal entropy production for the system where chemical reaction occurs and for the set of parallel heat engines are found.

We present a solution to the minimum time control problem for a classical harmonic oscillator to reach a target energy ET from a given initial state (qi, pi) by controlling its frequency ω, ωmin  ⩽ ω ⩽ ωmax . A brief synopsis of optimal control theory is included and the solution for the harmonic oscillator problem is used to illustrate the theory.

In this paper, the limiting performance of membrane systems with inhomogeneous composition is studied within the class of fixed rate processes. The problem of maintaining a nonequilibrium state in such a system using minimal power (separation problem) and the problem of extracting maximal power from such a system (diffusion engine problem) are formulated and solved. Results are obtained for diffusion engines with constant and periodic contact between the working body and the reservoirs.

While endoreversible heat-to-power conversion systems operating between two heat reservoirs have been intensely studied, systems with several reservoirs have attracted little attention. Here we analyse the maximum power processes of such systems with stationary temperature reservoirs. We find that independent of the number of reservoirs the working fluid uses only two isotherms and two infinitely fast isentropes/ adiabats. One surprising result is that there may be reservoirs that are never used. This feature is explained for a simple system with three heat reservoirs.

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The maximum power processes of multi-source endoreversible engines with stationary temperature reservoirs are investigated. We prove that the optimal solution is always time independent with a single hot and a cold engine contact temperature. The heat reservoirs fall into three groups: the hot reservoirs which are connected at all times for heat delivery, the cold reservoirs which are connected at all times for heat drain, and possibly a group of reservoirs at intermediate temperatures which are unused. This phenomenon is demonstrated for a three-source system. We find that for a commonly used class of heat transfer functions, including Newtonian, Fourier, and radiative heat transport, the efficiencies at maximum power are the same as for two-reservoir engines with appropriately chosen properties.