The Classical Smoluchowski Equation -- 2.The Quantum Smoluchowski Equation -- 3.Dynamics of Protons in DNA -- 4.The Interaction with the Environment -- 5.Classical and Quantum Mechanochemical Coupling -- 6.Photosynthesis and the quantum mechanochemical model -- 7.Entanglement, Coherence and Decoherence -- 8.Excitons -- 9.Long wavelength quantum energy exchange and its possible role in cellular recognition and communication -- A.Appendix.

In recent years, extensive research on stochastic processes such as neuron networks, molecular motors, dynamics models, anomalous diffusion, and disordered media has led to the development of various methods for applying the Classical and Quantum Smoluchowski Equation to these phenomena. This book focuses on presenting the solution to the Fokker-Planck equation using the Crank-Nicholson formalism. This method is particularly effective for handling systems with numerous interactions, requiring vector and matrix-oriented approaches suitable for implementation in Matlab. Among the topics treated in the book are: Dynamics of protons in DNA, Photosynthesis and the quantum mechanochemical model, Entanglement, coherence and decoherence, Excitons in the Fenna-Mathews-Olson complex, and Energy exchange between cells. The author has made an incredible work in facilitating the understanding of these complex topics. This book includes a brief and clear explanation of the Quantum theory and also includes code to build useful software to use in research environments. This volume is particularly helpful for graduate students in physics and biology interested in understanding biological processes with the use of quantum physics tools.