Limits to Fluctuation Dynamics
- URL: http://arxiv.org/abs/2309.07301v1
- Date: Wed, 13 Sep 2023 20:49:48 GMT
- Title: Limits to Fluctuation Dynamics
- Authors: Ryusuke Hamazaki
- Abstract summary: We show that the time derivative of the standard deviation of an observable is upper bound by the standard deviation of an appropriate observable describing velocity.
This indicates a hitherto unknown tradeoff relation between the changes for the mean and standard deviation.
Our results open an avenue toward a quantitative theory of fluctuation dynamics in various non-equilibrium systems.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The fluctuation of an experimentally measured observable, along with its
mean, constitutes the fundamental ingredient of a non-equilibrium system
involving randomness. Despite previous efforts, a comprehensive framework for
characterizing the temporal dynamics of fluctuations of observables remains
elusive. In this manuscript, we develop a ubiquitous theory concerning rigorous
limits to the rate of fluctuation growth. We discover a simple principle that
the time derivative of the standard deviation of an observable is upper bound
by the standard deviation of an appropriate observable describing velocity.
This indicates a hitherto unknown tradeoff relation between the changes for the
mean and standard deviation, i.e., the sum of the squares for these quantities
cannot exceed certain cost determined by dynamical processes. The cost can be
kinetic energy for hydrodynamics, irreversible entropy production rate for
thermodynamic processes, energy fluctuations for unitary quantum dynamics, and
quantum Fisher information for dissipative quantum dynamics. Our results open
an avenue toward a quantitative theory of fluctuation dynamics in various
non-equilibrium systems, encompassing quantum many-body systems and nonlinear
population dynamics, as well as toward our understanding of how to control
them.
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