Classical uncertainty relations and entropy production in non-equilibrium statistical mechanics
arXiv:2302.08290 · doi:10.1088/1742-5468/ace3b3
Abstract
We analyze Fürth's 1933 classical uncertainty relations in the modern language of stochastic differential equations. Our interest is motivated by applications to non-equilibrium classical statistical mechanics. We show that Fürth's uncertainty relations are a property enjoyed by martingales under the measure of a diffusion process. This result implies a lower bound on fluctuations in current velocities of entropic quantifiers of transitions in stochastic thermodynamics. In cases of particular interest, we recover an inequality well known in optimal mass transport relating the mean kinetic energy of the current velocity and the squared quadratic Wasserstein distance between the probability distributions of the entropy. In performing our analysis, we also avail us of an unpublished argument due to Krzysztof Gawȩdzki to derive a lower bound to the entropy production by transition described by Langevin-Kramers process in terms of the squared quadratic Wasserstein distance between the initial and final states of the transition. Finally, we illustrate how Fürth's relations admit a straightforward extension to piecewise deterministic processes. We thus show that the results in the paper concern properties enjoyed by general Markov processes.
25 pages, no figures
References in corpus (19)
- A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
- Thermodynamic uncertainty relation for biomolecular processes
- Measurements continuous in time and a posteriori states in quantum
- Refined Second Law of Thermodynamics for fast random processes
- Fluctuation Relations for Diffusion Processes
- Efficiency of molecular motors at maximum power
- Experimental study of the thermodynamic uncertainty relation
- Interference of Quantum Trajectories
- A unified, geometric framework for nonequilibrium protocol optimization
- On how nanomechanical systems can minimize dissipation
- E. Schrödinger's 1931 paper "On the Reversal of the Laws of Nature" ["Über die Umkehrung der Naturgesetze",Sitzungsberichte der preussischen Akademie der Wissenschaften, physikalische mathematische Klasse, 8 N9 144-153]
- On and beyond entropy production: the case of Markov jump processes
- Prescription-induced jump distributions in multiplicative Poisson processes
- Heat release by controlled continuous-time Markov jump processes
- On extremals of the entropy production by "Langevin-Kramers" dynamics
- On the efficiency of heat engines at the micro-scale and below
- Fluctuation Relations in Stochastic Thermodynamics
- R. Fürth's 1933 paper "On certain relations between classical Statistics and Quantum Mechanics" ["Über einige Beziehungen zwischen klassischer Statistik und Quantenmechanik", \textit{Zeitschrift für Physik,} \textbf{81} 143-162]
- Contextuality scenarios arising from networks of stochastic processes