In physics, equilibrium is a state in which the motion and internal energy of a system do not change over time. Videos of systems in balance would look exactly the same if watched in their normal chronological progression or in reverse. This symmetry means that a system has an entropy production rate of zero.
A physical phenomenon occurring out of equilibrium, on the other hand, would look different if it were to be observed chronologically or backwards. The entropy production rate of these non-equilibrium phenomena would therefore be greater than zero.
Previous studies have introduced several methods to calculate the rate of entropy production of simple systems out of equilibrium. However, a reliable method to measure this parameter in experimental contexts and in more complex systems has not yet been identified.
Researchers from Technion (Israel Institute of Technology), New York University and Princeton University have recently introduced a numerical method that can be used to derive local measures of the rate of entropy production. This method, presented in an article published in Physical examination lettersinvolves the comparison of particle trajectories in chronological and time-reversed simulations.
“We have studied non-equilibrium phenomena from the perspective of information theory, where our main interest has been to measure and evaluate the importance of the Shannon entropy of systems far from equilibrium. “said Dov Levine, one of the researchers who conducted the study. says Phys.org.
“This work is a natural extension of that, in that the essential feature of non-equilibrium systems is that they break time-reversal invariance (i.e., films look different forward and back).”
The technique developed by Ro, Guo and their collaborators essentially consists of analyzing videos showing the random movement of self-propelled particles in space. This movement is represented in a grid, where each point in the grid is assigned an integer that varies over time depending on the movement of the particles.
Subsequently, a model compares the representation of motion sequences in chronological order to those occurring in reverse time order, to determine the number of patterns shared between the two. These shared models are then used to estimate the entropy production rate of the system.
“We were able to measure entropy production (which is a direct consequence of breaking time-reversal invariance) by analyzing a movie (i.e. simulation) of an experiment,” said Levine said. “Motivated by previous work by the group of Mike Cates and his collaborators in Paris, we investigated the spatial dependence of this quantity (i.e. whether it is greater near walls or in regions of high density We then adapted an information theory method called “cross-analysis”, invented by Neri Merhav and Jacob Ziv, to measure a quantity directly related to the production of entropy.”
To demonstrate the effectiveness of their method, the researchers estimated the local entropy production of active Brownian particles undergoing what is known as “motility-induced phase separation” (i.e. a process in which the particles separate into a fluid phase of fast-moving particles, and clusters of slow motors), using numerical simulations. They also used it to estimate the entropy production rate of live E. coli bacteria, which were funneled into a specific region.
Their first results highlight the potential of this computational protocol to measure the entropy production rate of non-equilibrium phenomena in simulations and laboratory experiments. In the future, their proposed approach could open up exciting new possibilities for studying a wide range of complex dynamic systems, including bacteria, living tissues, cells, vortices, traffic, or other behaviors. collectives, and even cosmological phenomena.
“We showed that there is a connection between the amount of work that can be extracted from a region in a system and the amount of entropy production in that region,” Levine said. “Systems at equilibrium do not produce entropy and cannot do useful work, whereas systems far from equilibrium can. We are now trying to make the link between extractable work and production more precise. of entropy.”
Sunghan Ro et al, Model-free measurement of local entropy production and extractable work in active matter, Physical examination letters (2022). DOI: 10.1103/PhysRevLett.129.220601
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