{"id":"fa0bbc61-f377-439a-b47e-bfc301a04ce7","arxiv_id":"2506.01909","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"A greedy state-merging algorithm that maximizes retained irreversibility under coarse-graining preserves large fractions of entropy production and recovers place cells from hippocampal activity.","lead":"This paper introduces a model-free coarse-graining algorithm that merges states of a nonequilibrium system so as to lose as little irreversibility, or entropy production, as possible. Applied to motor-protein cycles, the Brusselator, and hippocampal calcium imaging, the method compresses thousands of states into a handful that retain much of the underlying dissipation and recover known biological structure.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Neural irreversibility is maximized at a timescale that may not resolve the underlying state-to-state dynamics, undermining the claim that the method uncovers a dissipative backbone.","rationale":"The paper's central formal claim is well posed: the iterative merge rule of Eq. (4) is a greedy algorithm whose objective is a measurable, nonnegative irreversibility drop. The derivations are straightforward and the kinesin enumeration check [Fig. 1(e)] provides genuine validation of the greedy optimum in a small system. The Brusselator and kinesin results demonstrate the procedure's practical value for known model systems. However, the strongest claim about real biological data—that the method recovers a spatial representation and uncovers the dissipative backbone of hippocampal activity—is not supported by the evidence as presented. The concern is not that the delay choice is outside consensus; it is that the delay is chosen by optimizing the very objective that the method then maximizes, without a control demonstrating that the recovered place-cell structure is insensitive to the construction parameter. Because the reader's weakest assumption identifies exactly this issue, I agree with the reader's assessment. The verdict remains CONDITIONAL: the paper is promising and technically sound in its model systems, but the neural application requires a robustness check before the central claim can be accepted.","tokens_in":10512,"tokens_out":1399,"duration_ms":12500,"concrete_test":"Recompute the neural CG for Δt over a dense range, e.g. 0.5, 1, 2, 3, 5, 10 s, and compare the resulting 10-state macrostates and the mutual-information curve. If the place-field structure and large-scale flux loop disappear or change substantially away from Δt=3 s, the neural conclusion is an artifact of the delay selection; if similar structures recur across an order of magnitude of Δt, the claim gains support.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central neural claim depends on the state construction: at each time point, the population state is the neuron that fired most recently, and a transition i→j is counted when neuron i precedes neuron j by a fixed delay Δt=3 s. The authors tune Δt to maximize the same irreversibility σ that their CG procedure then optimizes. If the so-constructed Markov chain is not a faithful state-space representation of the neural dynamics, then the recovered place-cell macrostates and the directed loop of flux [Fig. 3(c,e)] may be inherited from the delay-window construction rather than from an underlying dissipative structure. The circularity is direct: Δt is chosen to maximize σ (stated in the text), the optimal CG is defined to preserve σ, and the main evidence for 'efficient spatial representation' is the mutual information of the resulting CG. In the SM, the authors only report that other delays give qualitatively similar results, but no error bars, null controls, or shuffled-delay comparisons are shown. Because the CG procedure receives fluxes Jij computed from a chosen Δt, any choice of Δt can create an apparent cyclic flux; the claim that the hippocampus displays a large-scale dissipative backbone would require showing that the inferred structure is robust to the delay choice and not simply a consequence of optimizing the metric over the construction parameter.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes an iterative coarse-graining procedure for nonequilibrium systems: starting from measured fluxes between microscopic states, it repeatedly merges pairs of states whose combination causes the smallest drop in the local irreversibility measure defined by Eqs. (1)-(2). The procedure is tested on three systems: a four- and six-state kinesin chemical cycle, a Brusselator model with roughly 10^4 states, and hippocampal calcium-imaging recordings from a mouse running on a virtual track. In the kinesin case the greedy procedure is checked against exhaustive enumeration and matches the global optimum. For the Brusselator the procedure preserves far more irreversibility than random or square-block merging and partitions state space along the limit cycle. For the neural data, the procedure merges neurons into groups that resemble place cells, yields high mutual information between coarse-grained activity and position, and produces a directed loop of flux. The authors conclude that a model-free, irreversibility-preserving coarse-graining can reveal the dissipative backbone of a system directly from measured dynamics.","tokens_in":10794,"tokens_out":5120,"duration_ms":56011,"significance":"If the claims hold, the paper offers a practical, model-free tool for identifying large-scale dissipative structure from time-series data, with potentially broad applications in active matter, biochemistry, and neuroscience. The kinesin exhaustive check is a genuine strength, as is the clear formulation of the local merge cost in Eq. (4). The nontrivial part of the paper is not that the 'optimal' procedure outperforms random merging in preserving irreversibility—that is partly by construction—but that the resulting partitions recover meaningful physical structure (the Brusselator limit cycle, hippocampal place fields). The neural application is provocative and could be important, but it depends on a somewhat ad hoc delay-window construction of the Markov chain, and the circularity between delay selection and the optimization objective needs to be addressed before the strongest claims can be accepted.","major_comments":[{"comment":"The rule in Eq. (4) is a greedy, locally optimal rule: at each step it merges the pair with the smallest immediate irreversibility drop and then repeats. The manuscript nevertheless refers to the resulting partitions as 'optimal' throughout (e.g., Fig. 2 captions, Fig. 3 captions, and the main text 'the optimal CG'). Global optimality is verified only for the six-state kinesin model in Fig. 1(e), where exhaustive enumeration is possible. For the Brusselator (N ~ 10^4) and the neural data (N = 1485), no such verification is provided. Please rename the procedure 'greedy' or 'locally optimal' except where global optimality is proven, and state explicitly that for large systems the algorithm provides a heuristic that locally maximizes preserved irreversibility.","section":"Maximum irreversibility coarse-graining, Eq. (4)"},{"comment":"The choice of the delay window is coupled to the objective that the coarse-graining procedure maximizes. The text states, 'We use a time delay of Δt=3s, which we find produces neural dynamics with the largest irreversibility', and the CG procedure then preserves that same irreversibility. Since the state-space construction itself—most-recently active neuron with transitions counted within a fixed delay—can generate apparent cyclic flux, the central neural claims need additional support. Please provide (i) a shuffle control in which the ordering of neural firing events is randomized while the delay window is kept fixed, to show that the recovered place-cell structure and the macroscopic loop in Fig. 3(e) are destroyed; (ii) a scan over Δt showing that the ten-state partition, the place fields, and the mutual information in Fig. 3(d) are stable and are not simply the partitions that happen to best preserve the particular σ maximized by the delay choice; and (iii) confidence intervals on the irreversibility and mutual information curves, for instance from cross-validated flux estimates.","section":"Neural activity, Fig. 3"},{"comment":"For the Brusselator, the search is explicitly restricted to coarse-grainings that combine neighboring states: 'To preserve locality, we only consider CGs that combine neighboring states.' The red curve in Fig. 2(b) is therefore the best among neighboring-state merges, not the global optimum over all partitions. The comparison with random and square blocking remains informative, but the text should not imply that this is the globally optimal CG. Relatedly, the Introduction's statement that 'there is a unique coarse-graining with maximum irreversibility' is too strong; degeneracies in the merge costs can yield multiple CGs with the same preserved irreversibility, and the paper should say 'generically unique' or 'a coarse-graining' instead.","section":"Biochemical oscillator, Fig. 2(b)"},{"comment":"The description of the neural Markov chain is under-specified: the main text says the state is the most recent neuron to fire and that a transition i→j is counted when neuron i firing leads to neuron j firing after a time delay Δt = 3 s. This is ambiguous when several neurons fire within the delay window or when the same neuron fires repeatedly. The supplemental material should give the exact counting algorithm (e.g., how ties and repeated firings are handled, how the delay is applied relative to imaging frame boundaries), because the numerical values of the fluxes Jij, and hence the entire irreversibility measure, depend on this construction.","section":"Neural activity, state construction (main text and SM)"}],"minor_comments":[{"comment":"The axis labels '10°2', '10°1', '100' in the inset appear to be intended as powers of ten; please use standard superscript formatting (10^-2, 10^-1, 10^0).","section":"Fig. 2(b) inset"},{"comment":"Once the global-optimality language is adjusted, the captions should also use 'greedy' or 'locally optimal' instead of 'Optimal' to avoid overstating the result.","section":"Captions of Figs. 2 and 3"},{"comment":"The text mentions that the first macro-cell contains the majority of non-place cells, but this macro-cell is not visibly distinguished in the figure; please mark it or add a panel so the reader can identify which field is the uniform one.","section":"Fig. 3(c)"},{"comment":"A statement on code and data availability would be helpful, particularly for the neural analysis, so that the shuffle and delay-robustness checks can be reproduced by readers.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The manuscript's core idea is appealing and the kinesin exhaustive validation is convincing. The main risk is the neural application: the delay selection is tuned to the same objective that the method optimizes, and the current supplemental description is not enough to rule out an artifact. If the authors provide shuffle controls and delay scans with null expectations, the paper could become a strong candidate for publication. No concerns about novelty disclosure or citation practice beyond the need for a data availability statement."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The thing to know: this is a genuinely new prescription, not just an application — iterative greedy merging of states to minimize the local drop in irreversibility, Eq. (4), with a clean derivation from Esposito's inequality. The six-state kinesin check is the strongest part: exhaustive enumeration confirms the greedy result is globally optimal at every level, and the four-state model is a nice sanity check. The Brusselator result is visually striking, and the fact that the optimal partition follows the limit cycle rather than spatial blocks is a real observation.\n\nThe main soft spot is the neural application, and the stress-test concern lands. The state construction (most recent neuron to fire, transitions defined by a fixed delay Δt) is a modeling choice, and Δt = 3 s is chosen by maximizing the very same irreversibility that the CG procedure then preserves. That makes the headline “dissipative backbone” claim partly circular: any delay creates some cyclic flux, and optimizing the metric over that parameter can manufacture apparent structure. The authors say other delays give qualitatively similar results, but without error bars, null controls, or shuffled-delay comparisons in the main text — and with no supplemental material included — this cannot be checked. The mutual information comparison is also less clean than it looks: “optimal” is defined as the merge sequence that loses the least irreversibility, so beating random baselines on an irreversibility-related axis is guaranteed by construction. The spatial place-field recovery is suggestive, but it is one dataset, no error bars, and no code or data.\n\nA lesser but real issue: in large systems the greedy result is repeatedly called “optimal,” though only the kinesin case has a proof-by-exhaustion. That is a labeling problem, not a load-bearing flaw; the method is well-defined and the local rule is sensible. The “unique CG” sentence in the discussion is also stronger than what is shown — degeneracies and ties are not discussed.\n\nSumming up: the core algorithm and the kinesin validation are solid; the neural interpretation is oversold, and the manuscript as it stands does not ship the evidence needed to back it. Who gets value: stochastic thermodynamics people, and anyone doing data-driven coarse-graining of nonequilibrium time series. It deserves a serious referee — the idea is worth engaging — but the referee should push hard on the neural state construction, the Δt selection, and the missing reproducibility materials before publication.","headline":"A clean and useful greedy coarse-graining rule with a real validation on kinesin, undercut by a neural application whose state-space construction is circularly tuned.","tokens_in":11258,"tokens_out":2021,"would_cite":true,"duration_ms":19383,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Iteratively merging states that lose the least irreversibility recovers optimal coarse-grained dynamics, and in hippocampal data it rediscovers a place-cell map without positional information.","keywords":["irreversibility","coarse-graining","entropy production","nonequilibrium dynamics","Markov chains","place cells","hippocampus","renormalization group"],"falsifier":"Shuffle the order of neural transitions while preserving each neuron's firing rate and the empirical joint activity statistics, rerun the optimal coarse-graining, and check whether the macrostates still localize along the track: if shuffled data retain the place-cell structure and high spatial mutual information, the directed fluxes are not doing the work and the central claim fails; if the structure disappears, the claim survives.","tokens_in":1652,"feed_emoji":"🧠","tokens_out":2797,"duration_ms":100177,"temperature":0.7,"pith_summary":"The paper proposes that irreversibility itself is the right organizing principle for simplifying nonequilibrium dynamics. It defines a model-free coarse-graining that merges microstates in pairs, choosing at each step the merger that destroys the least local irreversibility, measured through steady-state fluxes. The paper shows that this procedure keeps as much dissipative information as possible in the reduced description, and demonstrates it on molecular-motor cycles, a biochemical oscillator, and hippocampal calcium imaging. In the neural data, the procedure groups neurons into macroscopic place cells whose firing encodes the mouse's position, even though no positional information is given to the algorithm.","feed_headline":"Maximizing irreversibility recovers place cells from neural data","feed_subtitle":"A model-free merge rule that keeps maximum dissipation rediscovers the mouse's spatial map from firing alone.","key_machinery":"The engine of the argument is the pairwise merge cost of Eq. (4), $\\Delta\\sigma_{\\alpha\\beta}$, which for candidate states $\\alpha$ and $\\beta$ subtracts the irreversibility lost when $\\alpha$ and $\\beta$ are fused, including both the flux directly between them and the changes in fluxes to all other states $\\gamma$. The procedure repeatedly merges the pair with the smallest such drop, starting from the measured fluxes $J_{ij}$ and steady-state probabilities; because total irreversibility can only fall under coarse-graining, the ordering of merges defines a sequence of macrostates that locally maximizes retained irreversibility at every scale. In the neural application the same rule is applied to a transition matrix inferred from spike timing, so the 'states' are neurons and the macrostates are subsets of the population.","core_discovery":"According to the paper, for any nonequilibrium system with measured steady-state fluxes, coarse-graining can only decrease the total irreversibility (the local entropy production associated with individual transitions), so for each target number of macrostates there is generically a coarse-graining that preserves as much of it as possible. Because searching over all partitions is combinatorially intractable, the paper introduces an iterative rule that merges the pair of states producing the smallest drop in irreversibility, and it reports that this greedy procedure finds the globally optimal coarse-graining in a six-state model where exact enumeration is possible. The paper's headline empirical claim is that applying this rule to hippocampal activity, modeled as a Markov chain over 'most recently active' neurons, yields macrostates that function as place cells, with a directed flux cycle matching the mouse's navigation, and that this structure arises without any access to position or behavior.","pith_inferences":["A natural next test is whether the same procedure recovers known latent variables in other neural recordings, such as head direction, decision variables, or replay sequences, where the ground-truth state is known independently.","The optimal coarse-graining is a form of lossy compression whose distortion measure is dissipation rather than prediction error; comparing it with information-bottleneck methods might clarify when maximally irreversible representations coincide with maximally predictive ones.","The greedy merge rule is not guaranteed to find the global optimum in large state spaces, so an open question is whether the place-cell structure in the hippocampus is exactly the global maximum-irreversibility partition or a local one that still retains most of the dissipative flux.","If the delay parameter $\\Delta t = 3$ s were chosen by the same irreversibility-maximization criterion, the method would become fully parameter-free in principle; testing different state constructions, such as population vectors instead of the most-recent-neuron state, would show how much of the recovered map depends on that choice."],"forward_implications":["Any dynamical time series can be coarse-grained without a model: fluxes alone define the merge order, so the procedure applies to systems whose underlying equations are unknown.","The preserved macrostates tend to organize around the dominant dissipative structures, such as the reaction cycle in kinesin, the limit cycle in the Brusselator, and the navigation loop in the hippocampus.","The neural result implies that irreversibility maximization can serve as an unsupervised way to discover meaningful latent variables, such as an animal's position, from collective activity alone.","The framework sets up the question of how much macroscopic irreversibility can survive coarse-graining in a given system, and whether consistent small-scale dissipative structures underlie large-scale function."],"supporting_citations":[{"why":"Establishes that coarse-graining can only reduce irreversibility, making the minimum-loss merge well-defined.","marker":"[31]"},{"why":"Defines the local irreversibility measure that the procedure maximizes as the objective.","marker":"[23]"},{"why":"Further develops local irreversibility in complex interacting systems, supporting the measure's use on neural dynamics.","marker":"[38]"},{"why":"Supplies the four-state kinesin-1 reaction-cycle model used as the first test case.","marker":"[39]"},{"why":"Supplies the six-state kinesin model that allows exact enumeration of all coarse-grainings to validate the greedy procedure.","marker":"[42]"},{"why":"Provides the Brusselator model of biochemical oscillations whose fluxes form the oscillator test case.","marker":"[43]"},{"why":"Provides the stochastic thermodynamics treatment of the Brusselator used for the biochemical application.","marker":"[44]"},{"why":"Supplies the hippocampal two-photon calcium-imaging dataset used for the neural application.","marker":"[46]"}],"fun_headline_variants":["Preserving irreversibility during coarse-graining yields place cells","Greedy state merging that retains irreversibility uncovers place cells","Retaining maximum dissipation in coarse-graining reveals spatial map","Coarse-graining to maximize irreversibility recovers hippocampal place cells","Irreversibility-preserving coarse-graining yields place cell activity"],"cache_read_input_tokens":13440,"weakest_assumption_plain":"The neural result rests on treating the recorded population activity as a Markov chain whose state is the most recently active neuron, with transitions defined by a fixed 3-second delay chosen to maximize irreversibility; if that construction misses the real dynamics, the recovered place-cell structure could be an artifact of the state definition rather than evidence about hippocampal irreversibility.","fun_headline_variants_meta":{"raw":{"variants":["Preserving irreversibility during coarse-graining yields place cells","Greedy state merging that retains irreversibility uncovers place cells","Retaining maximum dissipation in coarse-graining reveals spatial map","Coarse-graining to maximize irreversibility recovers hippocampal place cells","Irreversibility-preserving coarse-graining yields place cell activity"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000589,"raw_usage":{"total_tokens":2715,"prompt_tokens":845,"completion_tokens":1870,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":461,"completion_tokens_details":{"reasoning_tokens":1780}},"tokens_in":461,"tokens_out":1870,"duration_ms":12757,"temperature":1.0,"reasoning_tokens":1780,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T11:31:10.678690+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Shuffle the order of neural transitions while preserving each neuron's firing rate and the empirical joint activity statistics, rerun the optimal coarse-graining, and check whether the macrostates still localize along the track: if shuffled data retain the place-cell structure and high spatial mutual information, the directed fluxes are not doing the work and the central claim fails; if the structure disappears, the claim survives.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the local irreversibility measure that the procedure maximizes as the objective."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Further develops local irreversibility in complex interacting systems, supporting the measure's use on neural dynamics."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the four-state kinesin-1 reaction-cycle model used as the first test case."},{"cited_title":"Liepelt and R","cited_arxiv_id":null,"evidence_quote":"Supplies the six-state kinesin model that allows exact enumeration of all coarse-grainings to validate the greedy procedure."},{"cited_title":"Nicolis and I","cited_arxiv_id":null,"evidence_quote":"Provides the Brusselator model of biochemical oscillations whose fluxes form the oscillator test case."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the stochastic thermodynamics treatment of the Brusselator used for the biochemical application."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the hippocampal two-photon calcium-imaging dataset used for the neural application."}],"review_version":1}