Symmetry of physical laws Part I. Symmetry in space-time and balance theorems
MetadataShow full item record
In default of the theorem of "detailed balance": Pi;=P;i, with regard to elementary transition probabilities, several "balance" theorems are introduced and proved on the basis of symmetry of physical laws in space-time. (1) First theorem of "averaged balance" (Sec. 5) : We can establish P;;=P;; by averaging over quantities of "minus class." Table V (Sec. 3) gives a list of "minus" quantities. (2) The so-called "detailed balance of collisions" in classical physics is a special case of Theorem I. (3) Heitler-Coester's theorem of "semidetailed balance" is also a special case of Theorem I. (4) Second theorem of "averaged balance" (Sec. 5) : We can establish Pi;=P;; by averaging over quantities with PR= -1. The quantities with PR= -1 are listed in Table II (Sec. 2). (5) Theorem of "cyclic balance" (Sec. 7) : In classical physics, a chain of transitions i-->j-->k-->· ··-->i repeats itself cyclically. (6) Theorem of "long-range balance" (Sec. 7) : The time average of transition probability from i to j is equal to the time average of transition probability from j to i. Theorems I, II, and III, are direct consequences of inversibility (covariance for space-and-time inversion). Theorem IV is a consequence of reversibility (covariance for time reversal). Theorems V and VI are connected with ergodicity of Markoff's chains. This ergodicity is proved by the condition of bilateral normalization of transition probabilities: l:; P;;= 1, l:; Pi;= 1. This bilateral normalization in turn can be derived from either reversibility or inversibility. The limits of validity of all these balance theorems in actual applications are carefully examined in the text.
RightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
Showing items related by title, author, creator and subject.
On the Rate of Convergence for the Pseudospectral Optimal Control of Feedback Linearizable Systems Kang, Wei (2009);In this paper, we prove a theorem on the rate of convergence for the optimal cost computed using PS methods. It is a first proved convergence rate in the literature of PS optimal control. In addition to the high-order ...
Martinsen, Thor (Monterey, California. Naval Postgraduate School, 2007);Process Algebra forms a cornerstone in the formal methods area of Computer Science. Among the more widely used approaches is Milner's Communication and Concurrency Systems (CCS). Recently CCS has been extended by Schmidt ...
Hirsch, Charles; Dring, Robert P. (Monterey, California. Naval Postgraduate School, 1985-09); NPS67-85-012CRThe turbomachinery through-flow equations are reformulated for mass and momentum averaged quantities. The background of this analysis is the need for an improved assessment of the accuracy of through-flow computations. ...