10/6/2023 0 Comments Entropy is a measure ofA video may depict a wood fire that melts a nearby ice block, played in reverse it would show that a puddle of water turned a cloud of smoke into unburnt wood and froze itself in the process. For example, it is often very easy to tell the difference between a video being played forwards or backwards. Much like temperature, despite being an abstract concept, everyone has an intuitive sense of the effects of entropy. In thermodynamic systems that are not isolated, local entropy can decrease over time, accompanied by a compensating entropy increase in the surroundings examples include objects undergoing cooling, living systems, and the formation of typical crystals. Thus, entropy measurement is a way of distinguishing the past from the future. As one goes "forward" in time, the second law of thermodynamics says, the entropy of an isolated system can increase, but not decrease. Graduate Texts in Mathematics, vol.Use of the second law of thermodynamics to distinguish past from futureĮntropy is one of the few quantities in the physical sciences that require a particular direction for time, sometimes called an arrow of time. Walters, An Introduction to Ergodic Theory. 151 (Cambridge University Press, Cambridge, 2016) Cambridge Studies in Advanced Mathematics, vol. Weaver, The Mathematical Theory of Communication (The University of Illinois Press, Urbana, 1949) 2 (Cambridge University Press, Cambridge, 1984)Ĭ. Walters, Endomorphisms of a Lebesgue space. Ornstein, Ergodic Theory, Randomness and Dynamical Systems (Yale University Press, New Haven, 1973) 29 (University Gen ève, Geneva, 1981), pp. Monographies de L’Enseignement Mathématique, vol. Misiurewicz, Topological entropy and metric entropy, in Ergodic theory (Sem., Les Plans-sur-Bex, 1980). England, Mathematical Theory of Entropy, Encyclopedia of Mathematics and its Applications, vol. Mandelbrot, Fractal aspects of the iteration of z↦ λz(1 − z) for complex λ, z. Marcus, An Introduction to Symbolic Dynamics and Coding (Cambridge University Press, Cambridge, 1995)ī. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems (Cambridge University Press, Cambridge, 1995)ĭ. Goodwyn, Topological entropy bounds measure-theoretic entropy. Goodwyn, Comparing topological entropy with measure-theoretic entropy. Goodman, Relating topological entropy and measure entropy. Furstenberg, Disjointness in ergodic theory. Park, On the dynamics of polynomial-like mappings, Annales sci de l’É.N.S. Dinaburg, A correlation between topological entropy and metric entropy. De Villiers et al., Classification of papillomaviruses. Grundlehren der Mathematischen Wissenschaften (Springer, Berlin, 1982)Į. Hawkins, Rigidity of smooth one-sided Bernoulli endomorphisms. Page, The anatomy of a large-scale hypertextual web search engine. Stuck, Introduction to Dynamical Systems (Cambridge University Press, Cambridge, 2002) Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms. Billingsley, Ergodic Theory and Information (Wiley, New York, 1965) Dillner, International standardization and classification of human papillomavirus types. Batista, et al, An entropy-based approach for the identification of phylogenetically informative genomic regions of Papillomavirus. Weiss, The ergodic infinite measure preserving transformation of Boole.
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