To understand the forces at play in churn and retention dynamics, it’s best to think of your relationship with your customers as a marriage, and churn as divorce. Not because the metaphor is poetic, but for the practical reason that mathematics backs it up.
Economist José-Manuel Rey, in his paper A Mathematical Model of Sentimental Dynamics Accounting for Marital Dissolution, proposes that marital relationships follow a second law of thermodynamics. The paper claims that hey naturally erode over time unless sustained by a constant influx of effort.
This can be applied to many different kinds of relationships, including business-customer relationships.
Balancing feeling and effort
Relationships are dynamic systems with two variables:
- Feeling (how partners feel about the relationship)
- Effort (the energy invested to sustain it)
Rey’s formula aims to achieve ‘sentimental equilibrium’, a theoretical state in which a relationship is maintained at a constant level of both feeling and effort.
The effort gap
In banking, telecommunications, retail — everywhere — the default state of any relationship is entropy. If you are not actively strengthening relationships with your customers, they are weakening.
To counter this trajectory, effort is required. A key finding of Rey’s model is that the effort level required to maintain this equilibrium is always higher than the effort level that partners would naturally prefer or find most comfortable. This difference is called the “effort gap,” implying that a lasting relationship requires a permanent exertion of extra effort.
“The default state of any relationship is entropy. If you are not actively strengthening the relationship, it is weakening.”
However, there also comes a point where too much effort can cause an adverse effect. Rey’s theory of “effort utility” acknowledges that making a small amount of effort — such as planning an enjoyable activity with your partner — can be pleasant and emotionally rewarding for the effort-maker. However, once the required effort surpasses this optimal threshold, making additional effort begins to decrease a person’s utility and becomes emotionally costly. As the level of effort continues to increase beyond this point, a partner’s dissatisfaction goes up without bound.
In the context of a business-customer relationship, this effect mirrors the balance between cost and return on investment — you want to ensure the ‘effort’ (in this case, monetary investment) makes a positive enough impact to outweigh the cost.
Stability in an unstable system
Due to the unstable nature of external forces, partners must “continuously watch” their effort levels. Any change that causes a drop in effort (whether from internal relaxation or external pressure) must be corrected immediately. If partners are not alert to these changes, the relationship will drift onto a trajectory of deterioration.
The same goes for relationships between businesses and their customers. Factors unknown to the business affect customers’ lives on a daily basis, impacting their mood, and therefore their decision-making. To maintain a good relationship, businesses need a way to gather signals about an emotional change. Leading indicators of a change in emotion could be signalled by:
- Reduced usage velocity
- Delayed renewals
- Drop in engagement depth
- Lower response to outreach
- Increased support friction
Detecting the change is one thing, responding to it in a way that prevents looming churn is another. In a digital interaction environment, how you detect and respond to a stimulus is driven by algorithms. But if these algorithms cannot detect behavioral change signals, and respond to them with the optimal behavioral approach ,you will inevitably miss the opportunity to prevent churn.
This is why ecosystem.Ai’s customer interaction solutions are driven by behavioral algorithms including Sentimental Equilibrium, Loss Aversion, Prospect Theory and Risk Aversion. By detecting behavioral signals, our solutions can pinpoint changes in ‘emotion’, take real-time context and historical behavior into account, and respond with just the right amount of ‘effort’, at the right time, and in the right way.
Conclusion
Churn is not a sudden event — it is the visible outcome of gradual entropy. Like any relationship, customer loyalty decays when effort is misjudged, mistimed, or misdirected. The challenge is not simply to act, but to calibrate action: to detect subtle behavioral shifts, interpret them correctly, and respond with the right amount of effort before dissatisfaction compounds.
Behavioral intelligence makes this possible. By identifying early emotional signals and dynamically adjusting engagement, businesses can close the effort gap without overspending or overwhelming the customer. In doing so, they replace reactive retention tactics with proactive equilibrium — turning potential ‘divorces’ into durable, long-term partnerships.
