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Entropy- the key concept of thermodynamics finally newly developed and understandable §Using the classical approaches for the derivation of entropy It is not easy to understand this important concept of thermodyamics. This book presents a new and essentially better structured derivation and formulation which does not "put the cart before the horse" anymore and in this desription is suitable even for the basic university courses in thermodynamics. Entropy is the most important and at the same time most difficult to understand term of thermodynamics. Many people are discontent with its classical derivation since it is either based on "temperature" or "heat" which both can only exactly defined by entropy, or since it includes concepts such as "molecular disorder" which does not fit in a macroscopic theory. The physicists Elliott Lieb and Jakob Yngvason have recently developed a new description of thermodynamics which is free of these problems. It is based on the concept of adiabatic reachability, from which the principle of entropy can be derived in a direct, intuitionistic and understandable way. The principle of energy so takes over the central role of the main laws of thermodynamics, from which temperature can be derived and heat will be obsolete. The book includes seven illustrative examples of applications of entropy, which are presented step by step and explained in detail.