Nonequilibrium symmetry breaking

NONEQUILIBRIUM SYMMETRY BREAKING AND THE ORIGIN OF BIOMOLECULAR ASYMMETRY... 

The above example shows how a far-from-equilibrium chemical system can generate and maintain chiral asymmetry, but it only provides a general framework in which we must seek the origins of biomolecular handedness. The origin of biomolecular handedness, or life s homochirality, remains to be explained [11, 12]. Here we shall confine our discussion to how the theory of nonequilibrium symmetry breaking contributes to this important topic. We cannot yet say with confidence whether chiral asymmetry arose in a prebiotic (i.e. before life) process and facilitated the evolution of life, or whether some primitive form of life that incorporated both L- and D-amino acids arose first and subsequent evolution of this life form led to the homochirality of L-amino acids and D-sugars. Both views have their proponents. 

As for theoretical research on the chiral symmetry breaking, Frank was the first to show that a linear autocatalysis with an antagonistic nonlinear chemical reaction can lead to homochirality [16]. His formulation with rate equations corresponds to the mean-field analysis of the phase transition in a nonequilibrium situation [17], and other variants have been proposed [6, 18-23]. All these analyses have been carried out only for open systems where... 

Kondepundi, D. K. Nelson, G. W. (1983). Chiral symmetry breaking in nonequilibrium systems. Phys. Rev. Lett., 50, 1023-6. 

The article is divided in three parts. The first part consists of an introduction in the form of a general motivation. The second briefly presents some of the tools and techniques involved, thus forming the material of the next two sections. The third part of the series, spread over the last three sections, discusses three illustrative applications chosen from the field of statistical mechanics existence of certain phase transitions, symmetry breaking, and nonequilibrium. 

The plan of this chapter is the following. Section II gives a summary of the phenomenology of irreversible processes and set up the stage for the results of nonequilibrium statistical mechanics to follow. In Section III, it is explained that time asymmetry is compatible with microreversibility. In Section IV, the concept of Pollicott-Ruelle resonance is presented and shown to break the time-reversal symmetry in the statistical description of the time evolution of nonequilibrium relaxation toward the state of thermodynamic equilibrium. This concept is applied in Section V to the construction of the hydrodynamic modes of diffusion at the microscopic level of description in the phase space of Newton s equations. This framework allows us to derive ab initio entropy production as shown in Section VI. In Section VII, the concept of Pollicott-Ruelle resonance is also used to obtain the different transport coefficients, as well as the rates of various kinetic processes in the framework of the escape-rate theory. The time asymmetry in the dynamical randomness of nonequilibrium systems and the fluctuation theorem for the currents are presented in Section VIII. Conclusions and perspectives in biology are discussed in Section IX. 

On the other hand, the nonequilibrium steady states are constructed by weighting each phase-space trajectory with a probability which is different for their time reversals. As a consequence, the invariant probability distribution describing the nonequilibrium steady state at the microscopic phase-space level explicitly breaks the time-reversal symmetry. 

The chemical system discussed above is subject to a scalar nonequilibrium constant, namely the nonequilibrium concentrations of appropriate reservoir variables A, B,. ... This allows to consider an infinite system, for which no parameter related to the system size enters into the problem. Let us now briefly discuss the case of a nonequilibrium constraint which breaks the translational symmetry of the system. An example is provided by the diffusion of heat through a one-dimensional system of length L, parallel to the z-axis, whose end points a and b are maintained at different temperatures Tg and T. If one supposes that heat conduction following Fourier s law is the only transport mechanism taking place in the system, one verifies that the correlation function... 

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