Household and family systems

Family sociology describes households as role systems: who cooks, who earns, who regulates children, who holds secrets. Family systems therapy adds homeostasis — families resist change because the current dysfunction stabilises someone’s role. In FPE terms, a household is a level-\(L+1\) node whose \(\Phi\) is the nervous systems of its members and whose persistence depends on shared models staying cheap enough to coordinate.

Classical description

Concept	What it names
Emotional labour (Hochschild)	Invisible work of managing others’ affect and household mood
Identified patient	One member scapegoated as “the problem” while the system stays unchanged
Enmeshment / differentiation (Bowen)	Boundaries between self and family collapsed or healthy
Intergenerational transmission	Trauma, norms, and attachment patterns passed to children’s \(\Phi\)

Families persist not because everyone is happy but because \(\mathcal{R}^{(\text{household})} \ge 1\) — the pattern of roles, stories, and couplings continues as a recognisable node.

FPE mapping

A household IPS stores information in people, not in filing cabinets. Address, law, and dinner table are the Markov blanket; photos and deeds are pointers.

Term	Household reading
\(\Phi\)	Members’ health, regulation capacity, attachment, skills
\(P_{in}\eta\)	Income + attention spent on coordination (scheduling, childcare, repair)
\(\mathcal{D}_{KL}\)	Joint broadcast (“everything is fine”) vs private ISMs; secret affairs; money lies
\(\Gamma\)	Unresolved fights, role conflicts, unpaid emotional debts
\(\omega\)	Family “rules” nobody follows; ritual complexity without repair
\(\Psi\)	Extended kin, school, employer benefits, welfare state

Emotional labour as hidden numerator

Emotional labour is \(P_{in}\eta\) spent on others’ denominators — lowering \(\mathcal{D}_{KL}\) and \(\Gamma\) for the unit while the labourer pays the cost on their own ISM. When unevenly distributed, one member’s \(\mathcal{R}^{(L)}\) falls while the household looks stable — classic substrate export upward from individual to collective appearance.

Identified patient as \(\Gamma\) export

The identified patient holds unresolved friction for the subsystem so adults avoid operation 1+2 with each other. The child’s \(\Phi\) pays (symptoms, school failure, acting out) while parental \(\Gamma\) stays artificially low — same geometry as the drama triangle Victim at \(L+1\) scale (drama_triangle.md).

Intergenerational transmission as \(\Phi\) routing

Children are downstream \(\Phi\). When parents run high \(\mathcal{D}_{KL}\) or export \(\Gamma\) without repair, the next generation inherits:

higher default \(\Gamma\) in close coupling (attachment_and_coupling.md)
depleted \(\Phi\) (hypervigilance, chronic stress load)
learned priors that “truth is dangerous” or “repair never happens”

This is not determinism — but the fractal books close: parent persistence supervenes on child persistence (Theorem 5.3).

Why dysfunctions are stable

Dysfunctional equilibria persist when short-term \(\mathcal{R}\) for role-holders beats the cost of the two operations:

flowchart LR
  AvoidTruth["Avoid op. 1\n(D_KL hidden)"]
  AvoidRepair["Avoid op. 2\n(Gamma deferred)"]
  Export["Export to child\nor one partner"]
  Stable["Household looks\nstable today"]
  AvoidTruth --> Stable
  AvoidRepair --> Stable
  Export --> Stable

Each arrow is entropy export — someone else pays later.

Interruption

1. Lower \(\mathcal{D}_{KL}\)

Shared calendar truth: money, schedules, who is actually doing what.
Name observables in conflict: “When X happened, I felt Y” — not global labels.
Separate child’s node from marital node: don’t triangulate kids into \(\Gamma\).

2. Lower \(\Gamma\) — or decouple

Bounded repair conversations; one conflict per meeting.
Therapy as external \(\eta\) for operations the system cannot run alone.
Divorce or estrangement when \(C\) is large and repair refused — exit as \(\Gamma\) optimisation (voice_exit_loyalty.md).

3. Protect \(\Phi\)

Sleep, safety, and co-regulation for children before role reassignment.
Fair division of emotional labour — numerator must not drain one member’s \(\Phi\) permanently.

Clinical and structural footnotes

Real violence and coercion collapse \(\Psi\) for victims; “just communicate” fails when \(\Phi\) is under threat.
Poverty is low \(P_{in}\) at household layer — not a moral failure of “skills.”
Welfare state, childcare, and housing are \(\Psi\) for families — external shelter that lowers household \(\mathcal{E}_\Sigma\).