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Название: Entropy Calculated from the Frequency of States of Individual Particles
Автор: Alexandrowicz Z.
Entropy is related to the frequency of states for individual particles. Taking the Ising lattice as an example, a local state for an individual spin is defined by the orientation of the spin and of its neighbors. The ratio of the frequencies of two local states involved in a spin-flipping conflgurational transition is related to an entropy change. Implementation is by computer simulation. A stochastic process is used to construct an initial lattice configuration, corresponding to state of known entropy. This configuration is subsequently relaxed to a desired equilibrium state, with the help of a (uniform Metropolis) Monte Carlo spin flipping and the attendant entropy change is calculated from the sequence of frequency ratios for all transitions. The calculation is approximate since it treats a process that can be described by a hypothetical sequence of states at internal equilibrium, which cannot be true for a relaxation at finite rate. Nonetheless, the results obtained have been quite accurate. The theory, therefore, provides an additional method for measuring the entropy of systems simulated with the help of a computer. It also indicates a practical way for bridging the Boltzmann entropy of individual particle states (which Jaynes has shown to be incorrect, in its original form, for strongly interacting particles), to the Gibbs entropy ofN-particle configurations.