Thus, in thermodynamics, a'coarse-grain'set of partitions is defined which groups together similar microscopically different states and in " digital probabilistic physics " the specific microscopic state probability is considered alone.
12.
For an ideal polymer, as will be shown below, there are more microscopic states compatible with a short end-to-end distance than there are microscopic states compatible with a large end-to-end distance.
13.
For an ideal polymer, as will be shown below, there are more microscopic states compatible with a short end-to-end distance than there are microscopic states compatible with a large end-to-end distance.
14.
Thermal fluctuations are a basic manifestation of the temperature of systems : A system at nonzero temperature does not stay in its equilibrium microscopic state, but instead randomly samples all possible states, with probabilities given by the Boltzmann distribution.
15.
The most general answer is that the effect of thermal fluctuations tends to bring a thermodynamic system toward a macroscopic state that corresponds to a maximum in the number of microscopic states ( or micro-states ) that are compatible with this macroscopic state.
16.
When the number of possible microscopic states of thermodynamical systems is very large, it is inefficient to randomly draw a state from all possible states and accept it for the simulation if it has the right energy, since many drawn states would be rejected.
17.
First, for our ideal chain, a microscopic state is characterized by the superposition of the states \ vec r _ i of each individual monomer ( with " i " varying from " 1 " to " N " ).
18.
If the probabilities in question are the thermodynamic probabilities " p i " : the ( reduced ) Gibbs entropy ? can then be seen as simply the amount of Shannon information needed to define the detailed microscopic state of the system, given its macroscopic description.
19.
If the changes are sufficiently slow, so that the system remains in the same microscopic state, but the state slowly ( and reversibly ) changes, then is the expectation value of the work done on the system through this reversible process, " dw " rev.
20.
In 1877 Austrian physicist Ludwig Boltzmann described it more precisely in terms of the " number of distinct microscopic states " that the particles composing a macroscopic " chunk " of matter could be in, while still " looking " like the same macroscopic " chunk ".
