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Background
The standard Boltzmann-Shannon entropy is .
Plain-text mathematical notation (without MathML)
Background The standard Boltzmann-Shannon entropy is S(t)=−∑_(kl)(d)~_(kl)(t)log(d)~_(kl)(t).
Original LaTeX notation
Background
The standard Boltzmann-Shannon entropy is $S(t)=-\sum_{k l} \tilde{d}_{k l}(t) \log \tilde{d}_{k l}(t)$.step description prompt
To show the decreasing of entropy, we shall first simulate the dynamics and then calculate the entropy at each step. With the relative concentrations , we can use the standard Boltzmann-Shannon entropy. Define a function that returns this entropy at every step given the following: the monomer concentrations , the initial 2-mers concentration matrix , the ligation rate matrix lig, the process's timespan tf, and the number of simulation steps nsteps.
Plain-text mathematical notation (without MathML)
To show the decreasing of entropy, we shall first simulate the dynamics and then calculate the entropy at each step. With the relative concentrations (d)~_(ij)=d_(ij)/∑_(kl)d_(kl), we can use the standard Boltzmann-Shannon entropy. Define a function that returns this entropy at every step given the following: the monomer concentrations c₀, the initial 2-mers concentration matrix d₀, the ligation rate matrix lig, the process's timespan tf, and the number of simulation steps nsteps.
Original LaTeX notation
To show the decreasing of entropy, we shall first simulate the dynamics and then calculate the entropy at each step. With the relative concentrations $\tilde{d}_{i j}=d_{i j} / \sum_{k l} d_{k l}$, we can use the standard Boltzmann-Shannon entropy. Define a function that returns this entropy at every step given the following: the monomer concentrations $c_0$, the initial 2-mers concentration matrix $d_0$, the ligation rate matrix lig, the process's timespan tf, and the number of simulation steps nsteps.Discussion
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