Statistical physics of directional, stochastic chains with memory

TL;DR

This paper explores how memory effects influence the statistical properties of directional stochastic chains, revealing that assembly mechanisms significantly impact entropy and energy, with implications across various scientific fields.

Contribution

It introduces a sequence-dependent partition function to analyze systems with memory, extending traditional statistical physics approaches to directional chains.

Findings

Memory affects system statistics even in slow dynamics limit.

Entropy and internal energy vary due to memory effects.

Assembly mechanisms influence configurational order and information transfer.

Abstract

Stochastic chains represent a wide and key variety of phenomena in many branches of science within the context of Information Theory and Thermodynamics. They are typically approached by a sequence of independent events or by a memoryless Markov process. Here, we demonstrate that when memory is introduced, the statistics of the system depends on the mechanism by which objects or symbols are assembled, even in the slow dynamics limit wherein friction can be neglected. To analyse these systems, we introduce a sequence-dependent partition function, investigate its properties and compare it to the standard normalization defined by the statistical physics of ensembles. Then, we study the behaviour of the entropy and the internal energy in this intrinsic, directional chains finding that they vary around their thermally-induced equilibrium analogues due to memory effects. We anticipate that our results are necessary to interpret configurational order and information transfer in many molecular systems within Materials Science, Biophysics, Communication and Engineering.