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Register a new userThe Universal Arrow of Time I: Classical mechanics
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Statistical physics cannot explain why a thermodynamic arrow of time exists, unless one postulates very special and unnatural initial conditions. Yet, we argue that statistical physics can explain why the thermodynamic arrow of time is universal, i.e., why the arrow points in the same direction everywhere. Namely, if two subsystems have opposite arrow-directions at a particular time, the interaction between them makes the configuration statistically unstable and causes a decay towards a system with a universal direction of the arrow of time. We present general qualitative arguments for that claim and support them by a detailed analysis of a toy model based on the bakers map.
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A profound quest of statistical mechanics is the origin of irreversibility - the arrow of time. New stimulants have been provided, thanks to unprecedented degree of control reached in experiments with isolated quantum systems and rapid theoretical developments of manybody localization in disordered interacting systems. The proposal of (many-body) eigenstate thermalization (ET) for these systems reinforces the common belief that either interaction or extrinsic randomness is required for thermalization. Here, we unveil a quantum thermalization mechanism challenging this belief. We find that, provided one-body quantum chaos is present, as a pure many-body state evolves the arrow of time can emerge, even without interaction or randomness. In times much larger than the Ehrenfest time that signals the breakdown of quantum-classical correspondence, quantum chaotic motion leads to thermal [Fermi-Dirac (FD) or Bose-Einstein (BE)] distributions and thermodynamics in individual eigenstates. Our findings lay dynamical foundation of statistical mechanics and thermodynamics of isolated quantum systems.
The existence of a non-thermodynamic arrow of time was demonstrated in a recent paper (Mod.Phys.Lett. A13, 1265 (1998)), in which a model of non-local Quantum Electrodynamics was formulated through the principle of gauge invariance. In this paper we show that the Cosmic Microwave Background Radiation is capable of making every particle of the universe (except those which are not acted upon by an electromagnetic field) follow this arrow of time.
We introduce the special issue on the Statistical Mechanics of Climate published on the Journal of Statistical Physics by presenting an informal discussion of some theoretical aspects of climate dynamics that make it a topic of great interest for mathematicians and theoretical physicists. In particular, we briefly discuss its nonequilibrium and multiscale properties, the relationship between natural climate variability and climate change, the different regimes of climate response to perturbations, and critical transitions.
In this article, we discard the bra-ket notation and its correlative definitions, given by Paul Dirac. The quantum states are only described by the wave functions. The fundamental concepts and definitions in quantum mechanics is simplified. The operator, wave functions and square matrix are represented in the same expression which directly corresponds to the system of equations without additional introduction of the matrix representation of operator. It can make us to convert the operator relations into the matrix relations. According to the relations between the matrices, the matrix elements will be determined. Furthermore, the first order differential equations will be given to find the solution of equations. As a result, we unified the descriptions of the matrix mechanics and the wave mechanics.
Based on the assumption that time evolves only in one direction and mechanical systems can be described by Lagrangeans, a dynamical C*-algebra is presented for non-relativistic particles at atomic scales. Without presupposing any quantization scheme, this algebra is inherently non-commutative and comprises a large set of dynamics. In contrast to other approaches, the generating elements of the algebra are not interpreted as observables, but as operations on the underlying system; they describe the impact of temporary perturbations caused by the surroundings. In accordance with the doctrine of Nils Bohr, the operations carry individual names of classical significance. Without stipulating from the outset their `quantization, their concrete implementation in the quantum world emerges from the inherent structure of the algebra. In particular, the Heisenberg commutation relations for position and velocity measurements are derived from it. Interacting systems can be described within the algebraic setting by a rigorous version of the interaction picture. It is shown that Hilbert space representations of the algebra lead to the conventional formalism of quantum mechanics, where operations on states are described by time-ordered exponentials of interaction potentials. It is also discussed how the familiar statistical interpretation of quantum mechanics can be recovered from operations.
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