Relative Fluctuations in Density Blue Light Statistical Mechanics

Abstract

Whether by virtue of being prepared in a slowly relaxing, high-free energy initial condition, or because they are constantly dissipating energy absorbed from a strong external drive, many systems subject to thermal fluctuations are not expected to behave in the way they would at thermal equilibrium. Rather, the probability of finding such a system in a given microscopic arrangement may deviate strongly from the Boltzmann distribution, raising the question of whether thermodynamics still has anything to tell us about which arrangements are the most likely to be observed. In this work, we build on past results governing nonequilibrium thermodynamics and define a generalized Helmholtz free energy that exactly delineates the various factors that quantitatively contribute to the relative probabilities of different outcomes in far-from-equilibrium stochastic dynamics. By applying this expression to the analysis of two examples—namely, a particle hopping in an oscillating energy landscape and a population composed of two types of exponentially growing self-replicators—we illustrate a simple relationship between outcome-likelihood and dissipative history. In closing, we discuss the possible relevance of such a thermodynamic principle for our understanding of self-organization in complex systems, paying particular attention to a possible analogy to the way evolutionary adaptations emerge in living things.

• Received 23 December 2014

DOI: https://doi.org/10.1103/PhysRevX.6.021036

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

1. Research Areas

1. Physical Systems

1. Techniques

Statistical Physics

Authors & Affiliations

Nikolay Perunov, Robert A. Marsland, and Jeremy L. England

• Department of Physics, Physics of Living Systems Group, Massachusetts Institute of Technology, Floor 6, 400 Tech Square, Cambridge, Massachusetts 02139, USA

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Popular Summary

Humans are generally accustomed to explaining the many impressive functional adaptations exhibited by living things in Darwinian terms. In other words, heritable traits that help a creature survive and reproduce in a given environment get passed along to future generations. However, from the perspective of physics, we may also note that living things are universally good at latching onto sources of work energy in their environments (e.g., sunlight) and using that energy to dissipate heat into the surrounding air or water. We can accordingly consider the general situation of matter being driven by a source of work energy in contact with a heat bath. In doing so, we can demonstrate aspects of the physical properties of such a system that might help us to understand biological organization in a new light.

We put forth here a theoretical argument for a general tendency in driven matter to adopt shapes that have special histories of extra absorption of work energy from the environment. In particular, we consider two examples: a particle hopping around an energy landscape and a population of objects that self-replicate in an exponential fashion. We numerically show that a particle's (or population's) likely direction of evolution is correlated with the corresponding amount of absorption and dissipation of work. Put another way, we show that the probability of a particle or population ending up in a given macroscopic state is proportional to the thermodynamic flux that occurs on the way to that state. We are able to suggest a new thermodynamic perspective on self-organization far from thermal equilibrium that draws connections between the biological world and other systems governed by the same general physical principles.

We expect that our findings will pave the way for experimental studies of the nonequilibrium physics of lifelike behavior.

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Article Text

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References

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Issue

Vol. 6, Iss. 2 — April - June 2016

Subject Areas

• Biological Physics
• Complex Systems
• Statistical Physics

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Source: https://link.aps.org/doi/10.1103/PhysRevX.6.021036

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