Symmetry breaking, living systems

The problem of symmetry breaking (SB) is well known and multiply discussed in literature. Briefly, we can formulate it as follows. The Hamiltonian of any system of particles forming the Universe is totally symmetric with respect to rotations and reflections in the isotropic space-time, as well as transmutations of identical and equivalent particles, whereas the real objects of the material world composed by these particles do not possess such symmetry. This is seen already from the examples that we live in a world of particles, not antiparticles, and in condensed matter, we have mostly low-symmetry structures. This circumstance can be expressed by the statement that the world is in a state of broken symmetry. An obvious explanation of the contradiction between the totally symmetric Hamiltonian and the broken symmetry of the real world is that the latter is not a solution of its Schrodinger equation. 

Bifurcation, instability, multiple solutions, and symmetry-breaking states are all related to each other. Chemical cycles in living systems show asymmetry. The bifurcation of a solution indicates its instability, which is a general property of the solutions to nonlinear equations. 

The first important characteristic is that living systems are liquid crystalline. Liquid crystals are orientationally ordered molecular liquids. When a molecular liquid is in the isotropic liquid state (which models the primordial soup), it has neither translational nor orientational order. At the phase transition to the nematic state, the most basic liquid crystal transition, the system selects a special direction for long-range orientational order. This direction is called the director and denoted by a unit vector, n. By selecting a special direction, the nematic breaks the continuous rotational symmetry of the isotropic liquid. A phase boundary intervenes between the nematic and the isotropic liquid when they coexist. 

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