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We do not wish to construct a whole new game with new rules but to understand how Nature and human societies function.Ī well-known generalization of Boltzmann’s formula is Alfred Renyi’s suggestion. Beyond this, a demonstration is requested in the real world. It is required that the new suggestion must contain a case when the classical formula applies, and it must be clarified which of the original assumptions are invalidated. Entropy expressions were and are objects of long-term studies. Both the general validity of this concept and the generalized forms using probability. Indeed, entropy and its very formula have always been studied by several researchers. However, if someone intends to generalize the concept of entropy for more complex systems – like in a random network where “small world” effects are happening – then such modifying terms cannot be neglected any more. Such “finiteness effects” are light-heartedly neglected by theorists who discuss atomic systems. It also fails when the system under study is too small. Financial markets are comparable to the capricious behaviour of our atmosphere.Įxactly at the edge of chaos, where a dynamic system is just becoming chaotic, the classical logarithmic formula for entropy fails. Chaos poses limitations on predictability, the most cited example is the weather changed by a butterfly. ChaosĮntropy is related to chaos: i) an entropy formula expresses how the value of entropy depends on probabilities of alternative states, ii) the growth in entropy while elementary quantities change to and back, reflects the convexity of it, and iii) chaotic motion is a genuine producer of entropy.
#Entropy trial
The statistics of such dynamic processes stand the trial of time, as they deliver stationary probability density functions. Our own contemporary research reveals that entropy is also useful in the description of processes with dynamic equilibria when the detailed balance – the equity of rates in microscopic changes – fails, but a total balance of pluses and minuses is provided. It makes equilibrium to an optimal state of big systems built from many simple elements by simple rules. Permutation entropy by Ludwig Boltzmann is the logarithm of the number of interchanges on the microscopic level, leaving the macroscopic look unchanged. In energy technology, due to the interpretation of heat as molecular motion, entropy revealed itself as a concept describing complexity in general. Earth and the evolution of Life upon it is not a closed system. Here, the restriction in closed systems is important. The second law of thermodynamics dictates that the total entropy never decreases in a closed system. Entropy is an integral quantity, characterizing the totality of the motion, alike the “profit” characterizes the result of several complex processes in a single number. It describes motion in abstract parameter space, a trend, establishing the asymmetrical nature of the past and future. It was an analogy to “energy”, from the Greek “En-” meaning towards and “Tropos”, a place. The word “entropy” was coined in 1865 by Rudolph Clausius, a German professor of physics. Tamás Sándor Biró, Vice Director at the Wigner Research Centre for Physics, discusses the current status of entropy formula research