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Stochastic quantum dynamics

Jerzy Stryla

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

I propose to treat quantum evolution as a stochastic process consisting from a sequence of doubly stochastic matrices, which naturally arise in a generalized quantum evolution. Then it is proved that the law of non-decreasing entropy is fulfilled and that the law characterizes doubly stochastic matrices. An application of the model to support the generalized second law of black hole thermodynamics appears.

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arXiv:quant-ph/0509116•Sep 17, 2005•38 citations
I propose to treat quantum evolution as a stochastic process consisting from a sequence of doubly stochastic matrices, which naturally arise in a generalized quantum evolution. Then it is proved that the law of non-decreasing entropy is fulfilled and that the law characterizes doubly stochastic matrices. An application of the model to support the generalized second law of black hole thermodynamics appears.
Quantum-induced stochastic dynamics arises when a quantum system, strongly decohered by its coupling to a quantum environment, evolves as a genuine classical stochastic process. Depending on the environment's quantum state, the environment can act as a dynamic bath, capable of simultaneously exchanging heat and performing work. We formulate a thermodynamic framework for this semiclassical regime, defining heat, work, and entropy production. We derive a modified Second Law that accounts for nonequilibrium quantum features, such as squeezing. The framework is exemplified by an optomechanical setup, where we characterize the thermodynamics of the nonstationary noise induced by the cavity field.
Quantum-Induced Stochastic Dynamics arises from the coupling between a classical system and a quantum environment. Unlike standard thermal reservoirs, this environment acts as a dynamic bath, capable of simultaneously exchanging heat and performing work. We formulate a thermodynamic framework for this semi-classical regime, defining heat, work, and entropy production. We derive a modified Second Law that accounts for non-equilibrium quantum features, such as squeezing. The framework is exemplified by an optomechanical setup, where we characterize the thermodynamics of the non-stationary noise induced by the cavity field.
A general quantum theory encompassing Mechanics, Thermodynamics and irreversible dynamics is presented in two parts. The first part is concerned exclusively with the description of the states of any individual physical system. It is based on a new nonlinear quantum equation of motion, which reduces to the Schroedinger equation of motion of motion of conventional quantum dynamics only under special conditions. It accounts for the implications of the laws of Thermodynamics as well as for irreversible phenomena, such as the natural tendency of an isolated system to transit from any non-equilibrium state to an equilibrium state of higher entropy. Conversely, the laws of Thermodynamics and irreversibility emerge as manifestations of the fundamental quantum dynamical behaviour of the elementary constituents of any material system. We call this part Quantum Thermodynamics. The second part of the theory, which contains the first as a special case, is concerned with the description of stochastic distributions of states in an ensemble of identical physical systems each of which individually obeys the laws of Quantum Thermodynamics. It is based on a new measure-theoretic description of ensembles. It accounts unambiguously for the essential distinction between two types of uncertainties that are generally present in an ensemble, namely, quantal uncertainties due to the inherent quantal nature of the states of each individual member system and nonquantal uncertainties due to the stochastic distribution of states. We call this part Quantum Statistical Thermodynamics.