arXiv quant-ph/03111532003-11quant-ph

经典力学表述中的不确定性和信息。热力学和量子力学的共同点

Uncertainty and information in classical mechanics formulation. Common ground for thermodynamics and quantum mechanics

Adrian Faigon

备注：: Version 3. The whole article rewritten. Main content change is in Sections II.A to II.D: The main idea --the CPDQ principle for observables-- is obtained from an explicited property of the Lagrangian function. This property is shown to give rise to new principles from which Mechanics can be derived. 15 pages

摘要：

力学可以建立在一个原理上，这个原理将可观测粒子的轨迹中的不确定性Δ q与它相对于观测者的运动联系起来。根据这一原理，p. δ-q =常数，p是q-共轭动量，导出了力学定律，并讨论了拉格朗日函数和哈密顿函数的意义。文中还讨论了该原理与Hamilton的最小作用量原理之间的联系。波动力学和薛定谔方程出现没有额外的假设，通过选择的delta-q的情况下，运动的轨迹是不可描述的表示。Cramer-Rao不等式就是为了这个目的。对于一个隐藏的粒子从直接观察，位置的不确定性所确定的封闭边界导致热力学在一个简单的扩展所提出的形式主义。在经典力学表述中引入不确定性使得力学定律能够转化为信息论的广泛概念框架。经典力学、热力学和量子力学之间的界限是根据与系统演化相关的信息变化来定义的。作为一个直接的应用所提出的配方上界的信息传输速率推导。

英文摘要：

Mechanics can be founded on a principle relating the uncertainty delta-q in the trajectory of an observable particle to its motion relative to the observer. From this principle, p.delta-q=const., p being the q-conjugated momentum, mechanical laws are derived and the meaning of the Lagrangian and Hamiltonian functions are discussed. The connection between the presented principle and Hamilton's Least Action Principle is examined. Wave mechanics and Schrodinger equation appear without additional assumptions by choosing the representation for delta-q in the case the motion is not trajectory describable. The Cramer-Rao inequality serves that purpose. For a particle hidden from direct observation, the position uncertainty determined by the enclosing boundaries leads to thermodynamics in a straightforward extension of the presented formalism. The introduction of uncertainty in classical mechanics formulation enables the translation of mechanical laws into the wide ranging conceptual framework of information theory. The boundaries between classical mechanics, thermodynamics and quantum mechanics are defined in terms of informational changes associated with the system evolution. As a direct application of the proposed formulation upper bounds for the rate of information transfer are derived.

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