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Are the micro and the macro arrow of time connected each other

Piero Chiarelli

Published Jul 15, 2013• 0 citations
OpenAlex

Abstract

The connection between the micro and macro-arrow of time is discussed in the frame of the stochastic quantum hydrodynamic analogy. The presence of fluctuations that in the case on non-linear interactions leads to the breaking of the quantum mechanics on large scale and then to the macroscopic irreversibility and arrow of time, gives also rise to the time reversal breaking in the micro-scale quantum stochastic evolution (micro-arrow of time). The quantum irreversibility and the theoretical tools to calculate the time reversal asymmetry in the elementary particle decays are briefly discussed.

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The connection between the micro and macro-arrow of time is discussed in the frame of the stochastic quantum hydrodynamic analogy. The presence of fluctuations that in the case on non-linear interactions leads to the breaking of the quantum mechanics on large scale and then to the macroscopic irreversibility and arrow of time, gives also rise to the time reversal breaking in the micro-scale quantum stochastic evolution (micro-arrow of time). The quantum irreversibility and the theoretical tools to calculate the time reversal asymmetry in the elementary particle decays are briefly discussed.
The connection between the micro and macro-arrow of time is discussed in the frame of the stochastic quantum hydrodynamic analogy (SQHA). The presence of fluctuations that in the case on non-linear interactions leads to the breaking of the quantum mechanics on large scale and then to the macroscopic irreversibility with a defined arrow of time, gives also rise to the time reversal breaking in the micro-scale quantum evolution (micro-arrow of time). The quantum irreversibility with time reversal asymmetry is briefly discussed.
This paper presents a unified formulation of the origin of the arrow of time in classical and quantum mechanics. We begin with a mechanical analysis of a one-dimensional three-particle system, which provides a concrete example in which macroscopic irreversibility emerges despite microscopically reversible dynamics. By abstracting this mechanism, we identify coarse-graining as the essential ingredient responsible for macroscopic time asymmetry. We then formulate a general structural criterion for the thermodynamic arrow of time. We show that when microscopic time evolution forms a group while the induced macroscopic evolution forms only a semigroup, macroscopic time-reversal symmetry is necessarily broken. We prove that this semigroup structure arises if and only if the coarse-graining map from microscopic to macroscopic states is non-injective. This result holds independently of whether the underlying system is classical or quantum. In the quantum case, using density matrices, antiunitary time reversal, and CPTP coarse-graining maps, we show that macroscopic irreversibility follows inevitably from information loss, without requiring any asymmetry in the microscopic laws. Our results demonstrate that the thermodynamic arrow of time has a universal structural origin: the loss of microscopic information inherent in coarse-graining.
The paper investigates the non-local property of quantum mechanics in the quantum hydrodynamic analogy (QHA) given by Madelung. The role of the quantum potential in generating the non-local dynamics of quantum mechanics is analyzed. The work shows how in presence of noise the non-local properties as well as the quantization of the action are perturbed. The resulting stochastic QHA dynamics much depend by the strength of the interaction: Strongly bounded systems (such as linear ones) lead to quantum entangled stochastic behavior, while weakly bounded ones may be not able to maintain the quantum superposition of states on large distances and may loose their macro-scale quantum coherence acquiring the classical stochastic evolution . The work shows that in the frame of the stochastic approach it is possible to have freedom between quantum weakly bounded systems. The stochastic QHA model shows that the wave-function collapse to an eigenstates (deriving by interaction of a quantum microscopic system with a classical (macroscopic) one) can be described by the model itself as a kinetic quantum (relaxation) process to a stationary state. Since the time of the wave function decay to the eigenstate represents the minimum duration time of a measurement, the minimum uncertainty principle is shown to be compatible with the relativistic postulate about the light speed as the maximum velocity of transmission of interaction. About this topic, the paper shows that the Lorenz invariance of the relativistic quantum potential (coming from the Dirac equation) enforces the hypothesis that the superluminal transmission of information are not present in measurements on quantum entangled state.
I give an explanation of the thermodynamic arrow-of-time (namely entropy increases with time) within a quantum mechanical framework. This entails giving a solution to the Loschmidt paradox, i.e. showing how an irreversible macro-dynamics can arise from a reversible micro-dynamics. I argue that, in accordance to the reversible dynamics, both entropy-increasing and entropy-decreasing transformations take place, but entropy-decreasing transformations cannot leave any information of their having happened. This is indistinguishable from their not having happened at all. The second law of thermodynamics is then reduced to a tautology: the only transformations that can be seen are those where entropy does not decrease. However, typicality arguments seem to prevent this argument to be used as a complete solution to the arrow-of-time dilemma: it might still be necessary to postulate a low entropy initial state for the system under consideration.
The arrow of time paradox between quantum mechanics and thermodynamicsarises from the fundamental conflict between the time-symmetric evolution of thewave function and the irreversible increase of thermodynamic entropy. This pa?per introduces a ”small observer” model with quantum resolution capabilities andcombines quantum measurement theory with open quantum system dynamics toreveal the influence of observer scales on the perception of the arrow of time. Byestablishing a quantum master equation model for N coupled small observers, wedemonstrate the emergence of macroscopic thermodynamic entropy from micro?scopic quantum entropy production, providing a novel theoretical framework forunifying the understanding of the arrow of time. Numerical simulations based onthe quantum Darwinism framework validate the theoretical predictions.