4. Thermodynamics Tore Haug-Warberg, Long-Qing Chen, Ursula Kattner, Bengt Hallstedt, André Costa e Silva, Joonho Lee, Jean-Marc Joubert, Jean-Claude Crivello, Fan Zhang, Bethany Huseby, Olle Blomberg 4.1. Overview Thermodynamic modelling is software that uses thermodynamic calculations to predict the properties and behaviours of materials under various conditions. At its most basic, for example, thermodynamic modelling software provides information such as the melting point of an alloy, but in practice, the software is used to answer much more complicated and time-consuming questions about the behaviour of complex materials. Thermodynamic modelling is currently one of the most mature areas of ICME (Integrated Computational Materials Engineering), and companies that produce software tools for thermodynamic modelling are deeply involved in initiatives in the EU and US to advance the ICME vision, so thermodynamic modelling will likely continue to be an important part of many ICME projects. This chapter gives an overview of the current theory and practice of thermodynamic modelling. Sections 4.2 and 4.3 provide an introduction to some basic thermodynamic concepts and theory. Section 4.4 then gives an overview of the so-called CALPHAD (CALculation of Phase Diagrams) method, which is a thermodynamic modelling approach frequently used when it comes to solving practical material design problems that involve multi-component systems. In this approach, thermodynamic calculations provide the information on phases in stable or metastable equilibrium that are needed for predicting properties of materials under a wide range of temperature, pressure and composition conditions. Section 4.5 focuses on thermodynamic data, data formats and databases. The following section, 4.6, is concerned with how thermodynamic data and modelling can be integrated with modelling at larger scales. Section 4.7 then provides a set of examples of how thermodynamic modelling has been successfully used in various research and engineering projects. Section 4.8 contains a table of software tools and applications available for thermodynamic modelling, and the chapter concludes in section 4.9 with a list of recommended further reading. 4.2. Basic concepts and principles In thermodynamics, reality is simplified to the extent possible without sacrificing information about the static properties of the system. Thermodynamics builds on a system that is fully represented by a finite set of scalar, or sometimes tensorial, state variables. While these systems are adequate to describe the static properties of most solids, liquids and gases, it is not a fully dynamic model and, therefore, has limitations, e.g. natural fluctuations occurring within the system are not covered by the theory. A thermodynamic system has two extremes of complexity: general and simple. A general system description must aptly characterize micro- and nanostructures, anisotropic properties and