Resource limitations induce phase transitions in biological information processing
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Abstract
Biological information processing exhibits remarkable diversity across different organisms, which is presumably shaped by evolutionary optimization under limited resources. Starting from simple memoryless responses, more complex memory-based strategies may have evolved as resources became more available. In this Letter, we investigate minimal models of biological information processing under resource limitations by applying an optimal control technique proposed in [Tottori and Kobayashi, ]. We find that resource limitations such as sensing reliability, intrinsic stochasticity, and energy cost induce discontinuous phase transitions between memoryless and memory-based strategies, even though the minimal models fall within the standard linear-quadratic-Gaussian class. Moreover, these transitions can be nonmonotonic: Optimal information processing initially shifts from memoryless to memory-based strategies as sensing reliability increases, but then reverts to memoryless strategies if it increases further. Our results suggest that the complexity of biological information processing may be an evolvable trait that can switch back and forth between distinct strategies in a punctuated manner.
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At low energy availability (Q=100), the organism estimates the environmental state solely based on the current observation, corresponding to memoryless estimation.
“As a result, the organism estimates the environmental state x t solely based on the current observation y t , corresponding to memoryless estimation.”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [34]
The Phase Transition discussion (p. 3) says responsive estimation depends only on the instantaneous observation, supporting the memoryless-estimation part of the claim. It does not establish that this occurs at Q=100: the figure discussed there uses Q=10, and the model description (p. 2) defines Q as a weight on estimation error, not energy availability. (LLM, conf=0.86)
Experimental — accuracy not yet measuredAt low energy availability (Q=100), the memory control gains Π_zx and Π_zz vanish, indicating that no observational information is encoded into memory.
“At low energy availability ( Q = 100), the memory control gains, Π zx and Π zz , vanish, indicating that no observational information is encoded into the memory z t [Fig. 1(c,d)].”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [34]
The Phase Transition section (p. 3) says that when Π_zx = 0, memory does not accumulate past observations, supporting the claim's interpretation of that gain. Our copy does not report that both Π_zx and Π_zz vanish at Q = 100. Moreover, the Fig. 1 caption (p. 1) specifies Q = 10, not 100, so the cited figure does not establish the claimed condition. (LLM, conf=0.84)
Experimental — accuracy not yet measuredAt higher energy availability (Q=1000), Π_zx and Π_zz take nonzero values, and memory-based estimation becomes optimal.
“In contrast, when more energy is available ( Q = 1000), Π zx and Π zz take nonzero values, and memory-based estimation becomes optimal [Fig. 1(e,f)].”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [34]
The phase-transition discussion (p. 3) says memory-dependent estimation can become optimal, and the phase-diagram discussion (p. 3) links increasing Q to reduced resource constraints. But our copy does not report the claimed Q=1000 case or state that both Π_zx and Π_zz are nonzero there; its Fig. 1 caption (p. 1) lists panels (a–d), not (e,f). (LLM, conf=0.86)
Experimental — accuracy not yet measuredAt low Q, Π_zx = Π_zz = 0 is the only solution and is optimal.
“At low Q , Π zx = Π zz = 0 is the only solution and clearly optimal.”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [34]
The phase-transition discussion (p. 3) identifies the zero-Π_zx responsive strategy as optimal in one region, and Fig. 3 (p. 3) shows that the phase boundaries depend on Q/MF. Our copy does not state that at low Q both Π_zx and Π_zz are zero, or that this is the only solution. (LLM, conf=0.78)
Experimental — accuracy not yet measuredAfter further increase of Q, the optimal solution discontinuously switches from Π_zx = Π_zz = 0 to Π_zx, Π_zz ≠ 0.
“After further increase of Q , the optimal solution discontinuously switches from Π zx = Π zz = 0 to Π zx , Π zz = 0.”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [34]
On p. 3, the Phase Transition discussion reports a discontinuous switch from responsive to memory-dependent optimal strategies when memory-control cost M decreases. The phase-diagram discussion on p. 3 says increasing Q is nearly equivalent to decreasing M, supporting the proposed direction of the switch. Our copy does not explicitly establish the claimed joint change in both Π_zx and Π_zz as Q increases. (LLM, conf=0.77)
Experimental — accuracy not yet measured
As E increases, the current observation becomes less reliable, and memory-based estimation becomes favorable.
“As E increases, the current observation becomes less reliable, and memorybased estimation becomes favorable.”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [34]
On p. 3, the paper says that increasing observation noise E makes the observation less reliable and can shift the optimal strategy toward memory-dependent estimation. But its phase-diagram discussion on the same page reports a reverse transition at higher E: memory is advantageous only when observation noise is moderate. The claim omits that limit. (LLM, conf=0.87)
Experimental — accuracy not yet measuredIncreasing the observation noise E leads to a nonmonotonic transition.
“increasing the observation noise E leads to a nonmonotonic transition [Fig. 2(b)].”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [34]
The phase-diagram discussion (p. 3, Fig. 3) reports forward and reverse transitions as E increases, but only for fixed intrinsic noise F below a critical threshold. The cited Fig. 2(b) (p. 3) shows a switch from responsive to memory-dependent behavior, not the reverse transition that establishes nonmonotonicity. (LLM, conf=0.88)
Experimental — accuracy not yet measuredAs Q increases, nonzero Π_zx and Π_zz emerge discontinuously while Π_zx = Π_zz = 0 remains optimal.
“As Q increases, Π zx , Π zz = 0 emerge discontinuously, while Π zx = Π zz = 0 remains optimal.”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [34]
The phase-transition discussion (p. 3) reports that a memory-dependent solution with finite Π_zx emerges discontinuously while the responsive strategy remains globally optimal. But that result is shown as observation noise E increases, with Q fixed; the paper does not establish the same emergence for both Π_zx and Π_zz as Q increases. Its discussion of Q (p. 3) concerns phase boundaries and memory effect, not this specific sequence of solutions. (LLM, conf=0.84)
Experimental — accuracy not yet measuredThe phase boundaries with respect to Q, M, and F collapse onto a single curve when plotted against Q/MF, indicating a scaling relation among these parameters.
“Moreover, the phase boundaries with respect to Q , M , and F collapse onto a single curve when plotted against Q/MF [Fig. 2(c)], indicating a scaling relation among these parameters.”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [34]
On p. 3, the paper says the phase boundaries for F, M, and Q are “nearly identical” when plotted against Q/MF, supporting an approximate scaling relation. The claim’s unqualified “collapse onto a single curve” is stronger than that finding; p. 5 also says the scaling relation does not hold in the target-tracking problem. (LLM, conf=0.86)
Experimental — accuracy not yet measuredThe state noise D also induces a similar nonmonotonic phase transition.
“Furthermore, the state noise D also induces a similar nonmonotonic phase transition [33, 34].”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [34]
Increasing M or F induces a transition from memory-based to memoryless estimation.
“Similar to the transition with respect to Q , those with respect to M and F also occur monotonically but in the opposite direction: increasing M or F induces a transitions from memory-based to memoryless estimation [33, 34].”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [34]
Resource limitations induce a phase transition between memoryless and memory-based estimation strategies in a minimal model of biological information processing.
“By applying this framework to a minimal model of biological information processing, we found that resource limitations induce a phase transition between memoryless and memory-based estimation strategies [Fig. 1] [33, 34].”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [34]
The phase transition is discontinuous even though the model is linear and Gaussian.
“This phase transition is discontinuous even though this model is linear and Gaussian [Fig. 2(a)].”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [34]
The resource-induced phase transition exhibits discontinuity, nonmonotonicity, and a scaling relation even in a linear-quadratic-Gaussian setting.
“This transition also exhibits several nontrivial features, including discontinuity, nonmonotonicity, and a scaling relation, even in a linear-quadratic-Gaussian (LQG) setting [Fig. 2] [33, 34].”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [34]
At low E, memoryless estimation is optimal because the current observation contains sufficient information.
“At low E , memoryless estimation is optimal since the current observation contains sufficient information.”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [34]
When E becomes too large, memory control becomes ineffective, and memoryless estimation again becomes optimal.
“However, when E becomes too large, memory control becomes ineffective, and memoryless estimation again becomes optimal.”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [34]
Increasing Q induces a monotonic transition from memoryless to memory-based estimation.
“While increasing Q induces a monotonic transition from memoryless to memory-based estimation [Fig. 2(a)]”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [34]
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- Authors
- Tottori, T., & Kobayashi, T. J.
- Affiliations
- RIKEN Center for Brain Science (JP)
- The University of Tokyo (JP)
- Corresponding author
- Tottori, Takehiro
- Venue
- Physical Review Research
- Publisher
- American Physical Society (APS)
- Published
- 2025-10-14
- Volume
- 7
- Issue
- 4
- ISSN
- 2643-1564 (ISSN-L)
- OpenAlex
- W4415177698
- Cited by
- 3
- References
- 70
- Citations by year
- 2026: 2 · 2025: 1
- FWCI
- 0.91
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Physical Review Research (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University) (cc-by)
- Funders
- Japan Society for the Promotion of Science (22KJ0557, 19H05799, 24H02148, 24H01465, 25H01365)
- ACT-X (JPMJAX24LB)
- RIKEN
- Core Research for Evolutional Science and Technology (JPMJCR2011)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Systems and Dynamics
- Keywords
- biological information processing, resource constraints, phase transitions, memory-based strategies, optimal control, sensing reliability, intrinsic stochasticity, energy costs
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