Environmental-Driven Conditioning with Stochast Entropy Production

A paper combining the ideas in Stochastic Entropy Production (SEP) with Environment-Driven Conditioning (EDC)

1. Environmental-Driven Conditioning with
Stochastic Entropy Production (EDC{SEP):
A Diagnostic Framework for Quantum
Measurement
September 7, 2025
Abstract
Environmental-Driven Conditioning (EDC) provides an eective,
operational description of single-run quantum measurement dynamics
using stochastic Schrodinger equations (SSEs). A standard critique,
however, is circularity: conditioning presupposes denite records to
explain denite outcomes. In this paper we presentEDC{SEP, which
supplements EDC withstochastic entropy production(SEP) diagnos-
tics. Rather than claiming a resolution of circularity, we explicitly
reposition EDC{SEP as adiagnostic tool: SEP quanties irreversibil-
ity and thermodynamic cost, while redundancy measures quantify ro-
bustness of records. Together these diagnostics provide a framework
for analyzing quantum measurement processes from a thermodynamic
perspective. EDC{SEP oers experimentally accessible probes of the
interplay between information gain and entropy production, but it
does not solve the measurement problem.
Contents
1 Introduction
The measurement problem in quantum mechanics motivates a wide range of
interpretations and modications, from Everettian branching to objective col-
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2. lapse models such as GRW/CSL.Environmental-Driven Conditioning(EDC)
adopts a dierent stance: it is explicitlyeective, describing single-run con-
ditioned trajectories consistent with laboratory practice, without claiming to
provide a fundamental ontology.
EDC reproduces Born statistics via the martingale property of SSE tra-
jectories. However, critics emphasize that circularity remains: identifying
actual trajectories requires presupposing deniteness. To address this, we
propose augmenting EDC withstochastic entropy production(SEP) as devel-
oped in quantum stochastic thermodynamics. SEP quanties irreversibility
of trajectories through forward/backward path likelihood ratios.
In the present work, we reposition the combined framework|EDC{SEP|
as adiagnostic tool, not a solution. It provides measures of redundancy and
irreversibility that track when quantum measurement processesbehave as
ifoutcomes are denite. This reframing acknowledges the persistence of
circularity while highlighting the utility of thermodynamic diagnostics.
2 Stochastic Trajectories in EDC
We recall the EDC construction. A systemSwith HamiltonianHand mon-
itored observableLevolves under the conditioned SSE:
dj ti=


i
~
Hdt

2

L hLit

2
dt+
p


L hLit

dWt

j ti;(1)
withthe measurement strength anddWta Wiener increment.
Pointer projectorsPihave conditional probabilities
pi(t) =h tjPij ti; (2)
which are martingales withE[pi(t)] =pi(0). This ensures Born-rule consis-
tency. EDC uses such trajectories to model single experimental runs, but
does not claim to explain the origin of deniteness.
3 Stochastic Entropy Production
In stochastic thermodynamics, trajectory-level entropy production is dened
as
stot[] = ln
P[]
P
y
[
y
]
; (3)
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3. the log ratio of forward to backward path probabilities. This satises the
ensemble second law
hstoti 0: (4)
Applied to continuous quantum measurement, SEP provides a quantita-
tive measure of irreversibility associated with information acquisition. Im-
portantly, SEP is evaluated on the same stochastic trajectories that underlie
EDC, making the two frameworks naturally compatible.
4 The EDC{SEP Framework
4.1 Diagnostic Criteria
EDC{SEP introduces two diagnostics for analyzing measurement processes:
1.Redundancy:growth of mutual information across environment frag-
ments, quantifying robustness of records.
2.Entropy production:stotalong trajectories, quantifying thermo-
dynamic irreversibility.
When both redundancy and entropy production exceed empirical thresholds,
measurement processes behave eectively as if denite outcomes exist. These
criteria are diagnostic, not ontological.
4.2 Scaling Predictions
Both redundancy growth and entropy production rate scale with measure-
ment strength. EDC{SEP predicts monotone relations between, redun-
dancy, and entropy production, suggesting testable scaling laws in platforms
such as superconducting qubits and optical continuous monitoring.
4.3 Competing Observables
Simultaneous monitoring of non-commuting observables produces stationary
distributions rather than asymptotic lock-in. SEP remains nite without
diverging, suggesting that no stable redundancy threshold is achieved. This
regime illustrates how EDC{SEP diagnoses limitations of record formation.
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4. 4.4 Extension to QFT
Using Tomonaga{Schwinger evolution, local detector couplings, and spacetime-
indexed noise elds, EDC{SEP can be extended to relativistic settings. SEP
may then be dened locally as forward/backward path weight ratios for
detector-eld interactions, interpreted diagnostically rather than ontologi-
cally.
5 Conclusion
The EDC{SEP framework does not solve the measurement problem. Circu-
larity remains: the identication of actual trajectories and diagnostics pre-
supposes deniteness. What EDC{SEP does provide is a set ofpowerful
diagnostic toolsfor analyzing quantum measurement processes:
SSE trajectories capture single-run dynamics consistent with Born statis-
tics.
Redundancy measures quantify robustness of records.
SEP quanties thermodynamic irreversibility and cost of measurement.
Reframed as diagnostics, these tools support experimental investigations
of the interplay between information, thermodynamics, and measurement
strength. They complement|but do not replace|ontological approaches.
In this sense, EDC{SEP belongs to the same class as collapse models and
consistent histories: a valuable foil and diagnostic framework, not a nal
solution.
Acknowledgments
We thank C. L. Clarke and I. J. Ford for foundational work on stochastic
entropy production in quantum trajectories, which inspired this diagnostic
fusion.
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5. References
[1] C. L. Clarke and I. J. Ford, \Stochastic entropy production associated
with quantum measurement in a framework of Markovian quantum state
diusion,"arXiv:2301.08197, 2024.
[2] R. Marcus, \Environmental-driven selection by conditioning in quantum
measurement," unpublished manuscript, 2025.
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