Tropical limit in statistical physics

Tropical limit for macroscopic systems in equilibrium defined as the formal limit of Boltzmann constant k→0 is discussed. It is shown that such tropical limit is well-adapted to analyze properties of systems with highly degenerated energy levels, particularly of frustrated systems like spin ice and spin glasses. Tropical free energy Ftr(T) is a piecewise linear function of temperature T, tropical entropy is a piecewise constant function and the system has energy for which tropical Gibbs' probability has maximum. Properties of systems in the points of jump of entropy are studied. Systems with finite and infinitely many energy levels and phenomenon of limiting temperatures are discussed.