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An equivalent definition of entropy is the expected value of the self-information of a variable. [1] Two bits of entropy: In the case of two fair coin tosses, the information entropy in bits is the base-2 logarithm of the number of possible outcomes — with two coins there are four possible outcomes, and two bits of entropy. Generally ...
The statistical definition of entropy defines it in terms of the statistics of the motions of the microscopic constituents of a system — modelled at first classically, e.g. Newtonian particles constituting a gas, and later quantum-mechanically (photons, phonons, spins, etc.). The two approaches form a consistent, unified view of the same ...
Research concerning the relationship between the thermodynamic quantity entropy and both the origin and evolution of life began around the turn of the 20th century. In 1910 American historian Henry Adams printed and distributed to university libraries and history professors the small volume A Letter to American Teachers of History proposing a theory of history based on the second law of ...
The free energy principle is a mathematical principle of information physics: much like the principle of maximum entropy or the principle of least action, it is true on mathematical grounds. To attempt to falsify the free energy principle is a category mistake, akin to trying to falsify calculus by making empirical observations. (One cannot ...
This law of entropy increase quantifies the reduction in the capacity of an isolated compound thermodynamic system to do thermodynamic work on its surroundings, or indicates whether a thermodynamic process may occur. For example, whenever there is a suitable pathway, heat spontaneously flows from a hotter body to a colder one.
This quantity is the amount of entropy that may be increased without changing an internal energy or increasing its volume. [9] In other words, it is a difference between maximum possible, under assumed conditions, entropy and its actual entropy. It corresponds exactly to the definition of negentropy adopted in statistics and information theory.
The principle of maximum entropy is useful explicitly only when applied to testable information. Testable information is a statement about a probability distribution whose truth or falsity is well-defined. For example, the statements the expectation of the variable is 2.87. and + >
The low entropy of an ordered system can be viewed as an example of subjective emergence: the observer sees an ordered system by ignoring the underlying microstructure (i.e. movement of molecules or elementary particles) and concludes that the system has a low entropy. [16]