general entropy

entropy.tex

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 \begin{document}
 \maketitle
 \section{What is entropy?}
+Across disciplines, entropy is a measure of uncertainty or randomness.
+Originating in classical thermodynamics,
+over time it has been applied in different sciences such as chemistry and information theory.
+%As the informal concept of entropy gains popularity, its specific meaning can feel far-fetched and ambiguous.
+The name 'entropy' was first coined by german physicist \textit{Rudolf Clausius} in 1865
+while postulating the second law of thermodynamics.
+The laws of thermodynamics are based on universal observation regarding heat and energy conversion.
+Specifically, the second law states that not all thermal energy can be converted into work in a cyclic process.
+Or, in other words, that the entropy of an isolated system cannot decrease,
+as they always tend toward a state of thermodynamic equilibrium where entropy is highest for a given internal energy.
+Another result of this observation is the irreversibility of natural processes, also referred to as the \textit{arrow of time}.
+Even though the first law (conservation of energy) allows for a cup falling off a table and breaking
+as well as the reverse process of reassembling itself and jumping back onto the table,
+the second law only allows the former and denies the latter,
+requiring the state with higher entropy to occur later in time.
+
+Only 10 years later, in 1875, \textit{Ludwig Boltzmann} and \textit{Willard Gibbs} derived the formal definition
+that is still in use in information theory today.
+\begin{equation}
+S = -k_B \sum_i p_i \ln(p_i)
+\end{equation}
+It gives statical meaning to the macroscopical phenomenon by defining the entropy $S$ of a macrostate as 
+the result of probabilities $p_i$ of all its constituting micro states.
+
 \section{Definitions across disciplines}
 %- bedingte Entropie
 %- Redundanz