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The concept of entropy arose from Rudolf Clausius's study of the Carnot cycle which is a thermodynamic cycle ... to changes in the entropy and the external parameters.
In thermodynamics, a parameter representing the state of disorder of a system at the atomic, ionic, or molecular level; the greater the disorder the higher the entropy. [6] A measure of disorder in the universe or of the unavailability of the energy in a system to do work. [7] Entropy and disorder also have associations with equilibrium. [8]
The von Neumann entropy formula is an extension of the Gibbs entropy formula to the quantum mechanical case. It has been shown [ 1 ] that the Gibbs Entropy is equal to the classical "heat engine" entropy characterized by d S = δ Q T {\displaystyle dS={\frac {\delta Q}{T}}\!} , and the generalized Boltzmann distribution is a sufficient and ...
Despite the foregoing, there is a difference between the two quantities. The information entropy Η can be calculated for any probability distribution (if the "message" is taken to be that the event i which had probability p i occurred, out of the space of the events possible), while the thermodynamic entropy S refers to thermodynamic probabilities p i specifically.
The entropy of inhomogeneous systems is the sum of the entropies of the various subsystems. The laws of thermodynamics hold rigorously for inhomogeneous systems even though they may be far from internal equilibrium. The only condition is that the thermodynamic parameters of the composing subsystems are (reasonably) well-defined.
The entropy is thus a measure of the uncertainty about exactly which quantum state the system is in, given that we know its energy to be in some interval of size . Deriving the fundamental thermodynamic relation from first principles thus amounts to proving that the above definition of entropy implies that for reversible processes we have:
The concept of thermodynamic entropy arises from the second law of thermodynamics.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.
A new approach to the problem of entropy evaluation is to compare the expected entropy of a sample of random sequence with the calculated entropy of the sample. The method gives very accurate results, but it is limited to calculations of random sequences modeled as Markov chains of the first order with small values of bias and correlations ...