as: At zero temperature, the system must be in the state with the minimum thermal energy, the ground state. The constant value (not necessarily zero) of entropy at this point is called the residual entropy of the system. Note that, with the exception of non-crystalline solids (e.g., glasses) the residual entropy of a system is typically close to zero. However, it reaches zero only when the system has a unique ground state (i.e., the state with the minimum thermal energy has only one configuration, or microstate). Microstates are used here to describe the probability of a system being in a specific state, as each microstate is assumed to have the same probability of occurring, so macroscopic states with fewer microstates are less probable. In general, entropy is related to the number of possible microstates according to the Boltzmann principle where S is the entropy of the system, kB Boltzmann's constant, and Ω the number of microstates. At absolute zero there is only 1 microstate possible (Ω=1 as all the atoms are identical for a pure substance, and as a result all orders are identical as there is only one combination) and . Onsager relations The Onsager reciprocal relations have been considered the fourth law of thermodynamics. They describe the relation between thermodynamic flows and forces in non-equilibrium thermodynamics, under the assumption that thermodynamic variables can be defined locally in a condition of local equilibrium. These relations are derived from statistical mechanics under the principle of microscopic reversibility (in the absence of external magnetic fields). Given a set of extensive parameters (energy, mass, entropy, number of particles) and thermodynamic forces (related to intrinsic parameters, such as temperature and pressure), the Onsager theorem states that where are called the thermodynamic flows. See also Chemical thermodynamics Enthalpy Entropy production Ginsberg's theorem (Parody of the laws of thermodynamics) H-theorem Statistical mechanics Table of thermodynamic equations References Further reading Atkins, Peter (2007). Four Laws That Drive the Universe. OUP Oxford. Goldstein, Martin & Inge F. (1993). The Refrigerator and the Universe. Harvard Univ. Press. Guggenheim, E.A. (1985). Thermodynamics. An Advanced Treatment for Chemists and Physicists, seventh edition. Adkins, C. J., (1968) Equilibrium Thermodynamics. McGraw-Hill External links Scientific laws