On the law of increasing entropy and the cause of the dynamics irreversibility of quantum systems
It has been shown that time reversal symmetry breaking in the dynamics of large systems originates from symmetry breaking in the occupation of the Hilbert space. The states ϕ, for which the entropy of the system (sub-system) increases, are automatically created in nature or can be prepared experimentally, in contrast to the respective complex-conjugate states (ϕ*), for which the entropy decreases (although formally, according to the superposition principle, they can exist). It is indicated that, in the general case, the dynamics reversal of unknown states is impossible because the complex conjugation operator is antilinear. The complexity of reversal of the known state is exponential in the typical case of a large system. The formulated statements are illustrated by simple models.
Unable to display preview. Download preview PDF.
- 3.G. B. Lesovik and I. A. Sadovskyy, arXiv:1212.2576.Google Scholar
- 5.L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 5: Statistical Physics (Nauka, Moscow, 1995; Pergamon, Oxford, 1980).Google Scholar
- 9.D. I. Blokhintsev, Principles of Quantum Mechanics (Fizmatlit, Moscow, 1976; Allyn and Bacon, Boston, 1964).Google Scholar
- 12.In this case, the fact that the kinetic equation does not work “back in time” is seen already from the presence of ambiguity. Any of four initial states (or their superpositions) yields the same steady state. It is unclear to which particular initial state the kinetic equation could lead.Google Scholar
- 13.It should be emphasized that irreversibility (or hard reversibility) appears after the third step, rather than the second step, when relaxation to the equilibrium state (“thermalization”) has already occurred. Thus, the possibility of reversal in the quantum case is not determined by a mere entropy value (and the degree of entanglement is determined by the entropy insufficiently accurately).Google Scholar
- 14.Here, the analogy arises with one-way mathematical functions used in cryptography, for which y = f(x) can be easily calculated, whereas x = f −1(y) cannot. For clarity, we also indicate the example of an asymmetric distance which appears for travel in a city on streets with one-way traffic.Google Scholar