of quantum dynamics may be time-reversible, quantum processes are nondeterministic by nature. What state a wave function collapses into cannot be predicted mathematically, and further the unpredictability of a quantum system comes not from the myopia of an observer’s perception, but on the intrinsically nondeterministic nature of the system itself. In physics, the laws of motion of classical mechanics exhibit time reversibility, as long as the operator π reverses the conjugate momenta of all the particles of the system, i.e. (T-symmetry). In quantum mechanical systems, however, the weak nuclear force is not invariant under T-symmetry alone; if weak interactions are present reversible dynamics are still possible, but only if the operator π also reverses the signs of all the charges and the parity of the spatial co-ordinates (C-symmetry and P-symmetry). This reversibility of several linked properties is known as CPT symmetry. Thermodynamic processes can be reversible or irreversible, depending on the change in entropy during the process. See also Linear response function Green's function (many-body theory) Loschmidt's paradox Le Chatelier's principle - a nineteenth century principle that defied a mathematical proof until the advent of the Fluctuation Theorem. Crooks fluctuation theorem - an example of transient fluctuation theorem relating the dissipated work in non equilibrium transformations to free energy differences. Jarzynski equality - another nonequilibrium equality closely related to the fluctuation theorem and to the second law of thermodynamics Green-Kubo relations - there is a deep connection between the fluctuation theorem and the Green-Kubo relations for linear transport coefficients - like shear viscosity or thermal conductivity Ludwig Boltzmann Thermodynamics Brownian motor Notes References Statistical mechanics theorems Physical paradoxes Non-equilibrium thermodynamics