Abstract
An analogy between the thermodynamic inequalities presented by Nicholson et al. [Nat. Phys. 16, 1211 (2020)] and by Yoshimura and Ito [Phys. Rev. Res. 3, 013175 (2021)] is discussed. As a result, a time–energy uncertainty relation in chemical thermodynamics in terms of Gibbs free energy and chemical potential is derived. It is numerically demonstrated that the uncertainly relation holds in a model system of oscillatory Brusselator reactions. Our result bridges the thermodynamic time–information uncertainty relation and free energy evolution in chemical reactions.
Highlights
Stochastic thermodynamics has emerged as a comprehensive framework to understand the energetics and thermodynamics of stochastic processes away from equilibrium
It is not typically easy to quantitatively determine the entropy production associated with a nonequilibrium process without a detailed knowledge of the system
Yoshimura and Ito presented information geometric inequalities that give a speed limit for the changing rate of the Gibbs free energy and a general bound of chemical fluctuations, offering a framework to analyze the thermodynamic profile of biological systems
Summary
Stochastic thermodynamics has emerged as a comprehensive framework to understand the energetics and thermodynamics of stochastic processes away from equilibrium. Developed thermodynamics uncertainty relations provide a bound on entropy production in terms of current fluctuations.. Nicholson et al presented time–information uncertainty relations for the flux of heat, entropy, and work, demonstrating that the timescales of their dynamical fluctuations away from equilibrium are all bounded by the fluctuations in information rates and indicating that natural processes must trade speed for thermodynamic costs.. Yoshimura and Ito presented information geometric inequalities that give a speed limit for the changing rate of the Gibbs free energy and a general bound of chemical fluctuations, offering a framework to analyze the thermodynamic profile of biological systems.. We discuss an analogy between their thermodynamic inequalities and, derive a time–energy uncertainty relation in chemical thermodynamics in terms of Gibbs free energy and chemical potential Developed thermodynamics uncertainty relations provide a bound on entropy production in terms of current fluctuations. Nicholson et al presented time–information uncertainty relations for the flux of heat, entropy, and work, demonstrating that the timescales of their dynamical fluctuations away from equilibrium are all bounded by the fluctuations in information rates and indicating that natural processes must trade speed for thermodynamic costs. Yoshimura and Ito presented information geometric inequalities that give a speed limit for the changing rate of the Gibbs free energy and a general bound of chemical fluctuations, offering a framework to analyze the thermodynamic profile of biological systems. The formulations in Refs. 4 and 5 are built on the basis of a firm combination of finite-time thermodynamics and information geometry, with an employment of the Fisher information. In this paper, we discuss an analogy between their thermodynamic inequalities and, derive a time–energy uncertainty relation in chemical thermodynamics in terms of Gibbs free energy and chemical potential
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