small (of the order of 100 or 1000 molecules). The chemical Master equations is also solved for the very large models such as DNA damage signal, Fungal pathogen candida albicans for the first time. Quantum master equations A quantum master equation is a generalization of the idea of a master equation. Rather than just a system of differential equations for a set of probabilities (which only constitutes the diagonal elements of a density matrix), quantum master equations are differential equations for the entire density matrix, including off-diagonal elements. A density matrix with only diagonal elements can be modeled as a classical random process, therefore such an "ordinary" master equation is considered classical. Off-diagonal elements represent quantum coherence which is a physical characteristic that is intrinsically quantum mechanical. The Redfield equation and Lindblad equation are examples of approximate quantum master equations assumed to be Markovian. More accurate quantum master equations for certain applications include the polaron transformed quantum master equation, and the VPQME (variational polaron transformed quantum master equation). Theorem about eigenvalues of the matrix and time evolution Because fulfills and one can show that: There is at least one eigenvector with a vanishing eigenvalue, exactly one if the graph of is strongly connected. All other eigenvalues fulfill . All eigenvectors with a non-zero eigenvalue fulfill . This has important consequences for the time evolution of a state. See also Kolmogorov equations (Markov jump process) Continuous-time Markov process Quantum master equation Fermi's golden rule Detailed balance Boltzmann's H-theorem References External links Timothy Jones, A Quantum Optics Derivation (2006) Statistical mechanics Stochastic calculus Equations Equations of physics