![]() ![]() We find an explicitĮxpression for $S_B(\tau)$ in the limit $\Delta v \to 0$. Scaled with $\Delta v$ as: $t \sim \tau/\Delta v$. Surprisingly the different curves $S_B(t)$ collapse when time is The rate of approach depends on the size of $\Delta v$ in theĭefinition of the macrostate, going to zero at any fixed time $t$ when $\Delta $S_B(t)$Īpproaches its maximum possible value for the dynamical evolution of the given Time-evolved one-particle distribution associated with this ensemble. Nonequilibrium ensemble coincides with the Gibbs entropy of the coarse-grained Is large the Boltzmann entropy, $S_B(t)$, of a typical microstate of a We verify that when the number of particles Particles in rectangular boxes $\Delta x \Delta v$ of the single particle We define a macrostate $M$ by specifying the fraction of ![]() The construction requires one to define macrostates, corresponding to The free expansion of a one dimensional gas of non-interacting point particles. Download a PDF of the paper titled Entropy growth during free expansion of an ideal gas, by Subhadip Chakraborti and 3 other authors Download PDF Abstract: To illustrate Boltzmann's construction of an entropy function that is definedįor a microstate of a macroscopic system, we present here the simple example of
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