engleski

Relaxation of lineary coupled oscillators

Time development of the isolated ring of linearly coupled oscillators is found. The initial states are elements of the subensemble that is characterized with the fixed, nonuniform, distribution of oscillators amplitudes and equally weighted phases. Time development of the system, averaged over phase space, is calculated. The energies of oscillators are quantized. The probability of finding quantum of energy at a certain oscillator is proportional to the energy of an oscillator. Entropy of the system is described in terms of the distribution of energy quanta using the Shannon’ s definition of the information [1]. Numerical calculations show that entropy has a tendency to increase in accordance with the second law of thermodynamics. No entropy fluctuations during the relaxation process have been found. Entropy increases smoothly until the system reaches equilibrium. Then appear fluctuations. Single microscopic state is considered. Following Zurek [2] it is assumed that entropy can be assigned to this state. It is found that the time development of entropy is qualitatively same as in the case of the subensemble, i.e. entropy shows no fluctuation during the relaxation process. The distribution of the energies is calculated in the equilibrium state and it is found that it obeys Boltzmann distribution. [1] C. E. Shannon, The Mathematical theory of communication, University of Illinois Press, Chicago, 1998. [2] W. H. Zurek, Phys. Rev. A 40, 4731 (1989). [3] E. T. Jaynes, Phys. Rev. 106, 620 (1957). [4] E. T. Jaynes, Phys. Rev. 108, 171 (1957).

coupled oscillators; Shannon's entropy

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