2010/08/16 by Sarah Marzen, Marzen, Sarah, Dave Wu +7
Neuroscience · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Biological Physics (physics.bio-ph) #FOS: Physical sciences #Neural dynamics and brain function #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #physics.bio-ph
paper · pdf · doi:10.48550/arxiv.1008.2726
arxiv created 2010/08/16 · openalex publication_date 2010/08/16 · arxiv updated 2010/08/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Application of the information-theoretic Maximum Caliber principle to the microtrajectories of a two-state system shows that the determination of key dynamical quantities can be mapped onto the evaluation of properties of the 1-D Ising model. The strategy described here is equivalent to an earlier Maximum Caliber formulation of the two-state problem, but reveals a different way of imposing the constraints which determine the probability distribution of allowed microtrajectories. The theoretical calculations of second moments, covariances, and correlation times that are obtained from Maximum Caliber agree well with simulated data of a particle diffusing on a double Gaussian surface, as well as with recent experiments on a particle trapped by a dual-well optical trap. The formalism reveals a new relationship between the average occupancy of the two states of the system, the average number of transitions between the two states that the system undergoes, Markov transition probabilities, and the discretization time step. In addition, Maxwell-like relations imply how measurements on one potential landscape can be used to make predictions about the dynamics on a different potential landscape, independent of further experiment.