@ARTICLE{10.21494/ISTE.OP.2020.0497, TITLE={Time and space arrows: an understanding of the second law of thermodynamics}, AUTHOR={Bernard Guy, }, JOURNAL={Entropy: Thermodynamics – Energy – Environment – Economy }, VOLUME={1}, NUMBER={Issue 1}, YEAR={2020}, URL={https://openscience.fr/Time-and-space-arrows-an-understanding-of-the-second-law-of-thermodynamics}, DOI={10.21494/ISTE.OP.2020.0497}, ISSN={2634-1476}, ABSTRACT={The common formulations of the second law of thermodynamics link entropy and time in an almost exclusive way: "the entropy of an isolated system increases with time". This applies to both historical (Carnot, Clausius) and statistical (Boltzmann, Gibbs) formulations. This presentation does not facilitate an intuitive understanding of the entropy. Moreover, it does not allow us to see the conceptual unity behind two very different contents, one dealing with quantities of heat divided by temperatures, the other with a number of microscopic states ensuring the same macroscopic state. These difficulties are alleviated if we insist on the role of the spatial variable and its gradients. Thus the two usual formulations can be repeated in this sense, the first by saying that "heat naturally goes from hot to cold", and the second by saying that "an isolated heterogeneous system evolves in a more probable way towards homogeneity". This shows the conceptual unity of the second law: it expresses that, in an isolated system, heterogeneities, whether of temperature or other parameters, tend to decrease. Various topics are examined in the same frame: the notion of equilibrium, the question of time and space scales, the distinction between work and heat, the time problem etc.}}