| Abstract: |
| The question that we address during this talk is whether it is possible to determine if a linear chemical system satisfies the detailed balance property using measurements.
The property of detailed balance is a property of the chemical rates of chemical systems and it has an important physical meaning: active systems are modeled by equations that do not satisfy the detailed balance property, while passive systems are modeled by equations that satisfy the detailed balance property.
We assume that the chemical rates of the reactions in systems are not known and we assume that we can access information on the system via some measurements. A measurement $R_{ij}(t)$ is the concentration of the substance i at time $t>0$ after the injection of a substance j at time $t=0$. We obtain a condition involving reciprocal measurements (i.e. $R_{ij}(t)$ and $R_{ji}(t)$) that is necessary, but not sufficient for the detailed balance condition to hold in the network. Moreover, we prove that this necessary condition is also sufficient if a topological condition is satisfied, as well as a stability property that guarantees that the chemical rates are not fine tuned. |
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