The detailed balance property in chemical systemsCRC 1720: Early Career Seminar

by Eugenia Franco

Tuesday Jun 30, 2026, 2:15 PM → 3:15 PM Europe/Berlin

Endenicher Allee 60/2. OG.-040 - Room 2.040 (Mathezentrum)

The detailed balance property is a fundamental property that must be

satisfied by every chemical system that is at constant temperature and

that does not exchange chemicals and energy with the environment. Many

biochemical systems work in non-equilibrium conditions and exchange energy

and chemicals with the environment. As a consequence, they can be

effectively modeled using sets of equations for which the detailed balance

condition fails.

In this talk we will see that every (bidirectional) chemical system for

which the property of detailed balance fails can be obtained by freezing

the concentration of some substances in chemical systems for which the

detailed balance property holds. Moreover, we will see how to determine if

a linear biochemical system satisfies the detailed balance condition when

the details of all the reactions taking place are not known.

To this end, we use the formalism of response functions $R_{ij} (t)$ that

measure how the system reacts to the injection of the substance $j$ at time

$t=0$ by measuring the concentration of the substance $i$ for $t>0$. In

particular, we obtain a condition involving two reciprocal measurements

(that is $R_{ij} (t)$ and $R_{ji} (t)$) that is necessary, but not sufficient,

for the detailed balance condition to hold in the system. Moreover, we

prove that this necessary condition is also sufficient if a topological

condition is satisfied by the graph associated to the chemical system as

well as a stability property that guarantees that the chemical rates are

not fine-tuned.

 

The talk is based on joint works with B. Kepka and J. J. L. Velázquez.