Information-theoretic approaches to calculating thermodynamic entropy*

The thermodynamic entropy of matter equals (in suitable units) the Shannon information required to precisely specify its state. In a fully random substitutional alloy of N chemical species, log(N) bits of information per site are required to specify the site occupations. In an ideal gas of volume V, the information required to locate each molecule grows as log(V). If the alloy is not fully random, or the gas is not ideal, then prior information contained in positional correlations becomes redundant, and the thermodynamic entropy falls below its ideal value to a quantifiable extent. In this talk we will demonstrate this principle to calculate absolute entropies for liquid metals, vibrating solids, and high entropy alloys directly from simulated configurations without the need for thermodynamic integration.