Sum-over-all-paths with memory: Some applications from nm to Mm


  • Christopher Bernido Research Center for Theoretical Physics, Central Visayan Institute Foundation


For a stochastic variable x(s) the probability density function P(x,s;x₀,0) is solved in closed form by summing over all possible paths parametrized by a random white noise variable modulated by a memory function. We apply this white noise functional approach to fluctuating observables in complex systems ranging in scale from nanometer to Megameter. In particular, we investigate: (a) the distribution of nucleotides in bacterial genomes; (b) the motion of tracer particles embedded in an ageing fibrin polymer network; (c) the fluctuating values of protein diffusion coefficients as a function of protein length; and (d) the Great Barrier Reef degradation resulting from increasing atmospheric CO₂ levels and sea surface temperatures. Each case exhibits a particular memory behavior where a close match between empirical and theoretical mean square deviation (MSD) is obtained. For all cases, the probability density function satisfies a modified diffusion equation of the form

∂P/∂s = ½(∂MSD/∂s) (∂²P/∂x²).

The derived probability density function allows us to predict probable values of subsequent data points not yet measured, or to gain insight on the dynamics and memory property of the systems considered.

About the Speaker

Christopher Bernido, Research Center for Theoretical Physics, Central Visayan Institute Foundation

Christopher C. Bernido is presently the President of the Central Visayan Institute Foundation (CVIF). He obtained his Ph.D. (Physics) in 1982 and M.S. (Physics) in 1979 from the State University of New York at Albany, USA, and B.S. (Physics) degree from the University of the Philippines (UP) at Diliman in 1977. He was conferred the degrees Doctor of Humanities (honoris causa) by the Holy Angel University (2012) and Doctor of Pedagogy (honoris causa) by Ateneo de Naga University (2014).
Chris was a Research Fellow of the Alexander von Humboldt Foundation in Germany from 1987 to 1989. From 1996 to 2001, he was also a Senior Associate Member of the International Centre for Theoretical Physics in Trieste, Italy.
Chris taught for 17 years at UP Diliman where he got the Chancellor’s Award for Outstanding Researcher and Teacher in 1995. He was the Director of the National Institute of Physics in UP from 1983-1986, and served as President of the Samahang Pisika ng Pilipinas (SPP, Physical Society of the Philippines) from 1984-1987. In 2016, he was elected Fellow of the SPP. He received in 1987 the Achievement Award in Physics from the National Research Council of the Philippines. He was elected member of the National Academy of Science and Technology of the Philippines in 2007.
Together with his wife Maria Victoria, they were given the Ramon Magsaysay Award in 2010 for improving basic education in the Philippines through their CVIF Dynamic Learning Program.



Article ID



Invited Presentations



How to Cite

C Bernido, Sum-over-all-paths with memory: Some applications from nm to Mm, Proceedings of the Samahang Pisika ng Pilipinas 37, SPP-2019-INV-1D-01 (2019). URL: