Energy 26 (2001) 307–319 www.elsevier.com/locate/energy Principles of control thermodynamics P. Salamon a,* , J.D. Nulton b , G. Siragusa c , T.R. Andersen d , A. Limon a a Department of Mathematical and Computer Sciences, San Diego State University, 5300 Campanile Drive, San Diego, CA 92182, USA b Department of Mathematics, San Diego City College, San Diego, CA 92101, USA c Department of Chemistry, San Diego State University, 5300 Campanile Drive, San Diego, CA 92182, USA d CAPEC, Department of Chemical Engineering, Technical University of Denmark, DK-2800 Lyngby, Denmark Received 28 September 1999 Abstract The article presents a partial synthesis of progress in control thermodynamics by laying out the main results as a sequence of principles. We state and discuss nine general principles (0–8) for finding bounds on the effectiveness of energy conversion in finite-time.  2001 Elsevier Science Ltd. All rights reserved. 1. Introduction This article presents a synthesis of progress using a particular approach to the meaning of time for thermodynamic processes. The approach captures one aspect of the flavor of traditional thermodynamics: that of providing bounds. Our aim is to understand the limiting role of time in a thermodynamic process. Specifically, our quest is to understand the limits to energy conversion processes in which the time evolution is only partially specified, i.e. the sequence of states tra- versed by some part of the system is given. We then ask the question: Of what total process might this given time evolution of our subsystem be a part? In general there are many possible answers to this question. One of the goals of the endeavors described below is to examine the mathematical structure of this set of possible co-evolutions of our subsystem and its sequence of environments. In particular, we look for extreme points in this set; notably ones that maximize work or minimize entropy production. As a simple example, consider the operation of a heat engine in which a gaseous working fluid traverses a given cycle as specified by a quasistatic locus in its (p,V) plane, i.e. by an indicator diagram. This example in various guises has resurfaced in * Corresponding author. E-mail address: salamon@math.sdsu.edu (P. Salamon). 0360-5442/01/$ - see front matter  2001 Elsevier Science Ltd. All rights reserved. PII:S0360-5442(00)00059-1