{"id":"86d2d9b3-b52a-4434-a525-6a12f4cec56b","arxiv_id":"2605.10099","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Conditional non-Hermitian Jarzynski equality holds under parity-exchange symmetry across an SU(2)-rotated family of hybrid PT-APT two-level systems, verified at three experimental points.","lead":"This paper shows that a conditional non-Hermitian Jarzynski equality holds in hybrid PT-APT two-level systems when transition probabilities satisfy parity-exchange symmetry, and that this symmetry persists under SU(2) rotations. A smart generalist might read it to see how symmetry conditions can extend thermodynamic equalities into non-Hermitian quantum regimes with experimental checks in trapped ions.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's weakest_assumption matches the paper's explicit restriction. The symmetry persistence is presented as the technical advance and is supported by stated arguments plus targeted experiment; nothing in the provided material indicates that this support is insufficient or circular within the two-level postselected setting.","tokens_in":1808,"tokens_out":249,"duration_ms":14233,"concrete_test":"Recompute the transition probabilities for an intermediate point (e.g., theta = pi/6) directly from the linear combination of PT and APT terms and verify whether the parity-exchange symmetry relation holds identically to the endpoints.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is explicitly conditional on the postselected no-quantum-jump framework and asserts that parity-exchange symmetry of transition probabilities is preserved under the full SU(2) orbit of the hybrid PT-APT Hamiltonians. The abstract states that this preservation is shown by complementary geometric and algebraic arguments in the two-level setting, with experimental checks at the three representative points. No unstated assumption, internal inconsistency in the symmetry argument, or mismatch between the claimed orbit and the checked points is apparent from the given description.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript claims that, within a postselected no-quantum-jump framework, a conditional non-Hermitian Jarzynski equality holds for two-level hybrid PT-APT Hamiltonians provided the transition probabilities satisfy a parity-exchange symmetry. Complementary geometric and algebraic arguments are used to show that this symmetry is preserved under the full SU(2) orbit of the hybrid family. Three representative points (θ = 0, π/4, π/2) are implemented experimentally in a trapped 171Yb+ ion, where work distributions are measured for cyclic protocols with ΔF = 0 and the predicted equality is reported to hold.","tokens_in":1885,"tokens_out":494,"duration_ms":21050,"significance":"If the central symmetry argument and its experimental checks are valid, the work extends the domain of the conditional non-Hermitian Jarzynski equality from isolated PT-symmetric endpoints to a continuous hybrid PT-APT family. The combination of an orbit-wide symmetry proof with trapped-ion verification at representative points constitutes a concrete advance within the restricted two-level, postselected setting. The result remains conditional on the no-jump postselection and the two-level restriction, which limits immediate generality but supplies a clear, testable criterion.","major_comments":[],"minor_comments":[{"comment":"Abstract and §2: the precise definition of the parity-exchange symmetry (i.e., the relation between P(forward) and P(reverse) under the PT-APT exchange) should be stated explicitly before the geometric/algebraic arguments are invoked, so that the reader can verify the claimed persistence without ambiguity.","section":"Abstract, §2"},{"comment":"Experimental section: the work distributions and error bars for the three measured points are referenced but not shown in the provided text; inclusion of the raw histograms or at least the extracted ratios with uncertainties would allow direct assessment of the confirmation at θ = 0, π/4, π/2.","section":"Experimental section"},{"comment":"Notation: the parameter θ that parametrizes the SU(2) orbit is introduced but its range and the explicit form of the hybrid Hamiltonian H(θ) are not written out in the abstract; a compact equation for H(θ) early in the manuscript would improve readability.","section":null}],"recommendation":"minor_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the careful reading and positive assessment of our manuscript on the symmetry-enforced conditional non-Hermitian Jarzynski equality. The referee correctly identifies the central advance as extending the symmetry criterion from isolated PT endpoints to the full SU(2) orbit of hybrid PT-APT two-level systems, together with experimental verification at three representative points. No major comments were raised in the report.","responses":[],"tokens_in":1354,"tokens_out":99,"duration_ms":10053,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main advance is showing that the parity-exchange symmetry needed for the conditional non-Hermitian Jarzynski equality survives the entire SU(2) rotation that mixes PT and APT terms, not just at the pure PT endpoint. They back this with geometric and algebraic arguments in the two-level case and then run the cyclic protocol on three representative Hamiltonians in a trapped Yb+ ion, measuring work distributions that line up with the predicted equality when Delta F is zero.\n\nThe experimental part is straightforward and directly tests the symmetry criterion at theta = 0, pi/4, pi/2. That gives concrete data points rather than pure theory. The framing is also clear about staying inside the postselected no-jump regime, so the claim is not oversold as a general non-Hermitian result.\n\nThe soft spot is that everything remains conditional on postselection and the two-level restriction. The abstract does not indicate how the symmetry would behave if quantum jumps were included or in larger systems, and the experiments only sample three discrete points even though the argument is for the continuous family. Without the full derivations it is hard to judge whether the geometric and algebraic steps close without extra assumptions.\n\nThis is for people already working on non-Hermitian thermodynamics or PT-symmetric systems in trapped ions. It is a modest but concrete extension of earlier PT-only results. It deserves peer review because the combination of symmetry argument and experimental check is worth a referee's time, even if revisions will be needed on scope and detail.","headline":"The paper extends a conditional Jarzynski equality to the full SU(2) orbit of hybrid PT-APT two-level systems by showing parity-exchange symmetry persists, with ion-trap checks at three points.","tokens_in":2400,"tokens_out":392,"would_cite":false,"duration_ms":10270,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"In postselected no-jump dynamics, parity-exchange symmetry enforces a conditional non-Hermitian Jarzynski equality across an SU(2) family of hybrid PT-APT Hamiltonians.","keywords":["non-Hermitian Jarzynski equality","PT symmetry","APT symmetry","postselection","quantum thermodynamics","trapped ions","SU(2) rotation","parity-exchange symmetry"],"falsifier":"An experiment that measures work distributions in a hybrid PT-APT system whose transition probabilities violate parity exchange yet still satisfy the conditional Jarzynski equality would falsify the necessity of the symmetry.","tokens_in":2692,"feed_emoji":"⚛","tokens_out":692,"duration_ms":22074,"temperature":0.7,"pith_summary":"The paper shows that a conditional Jarzynski equality linking work statistics to free-energy differences can be recovered in non-Hermitian two-level systems when the transition probabilities satisfy a parity-exchange symmetry. This symmetry is preserved under the full family of Hamiltonians obtained by SU(2) rotations that mix parity-time and anti-parity-time terms. A sympathetic reader would care because the result extends earlier PT-only statements to a continuous orbit of hybrid cases while remaining inside the restricted postselected framework. Complementary geometric and algebraic arguments establish the symmetry invariance, and the claim is tested by preparing three points in the family inside a trapped ytterbium ion and recording work distributions for zero free-energy-change cycles.","feed_headline":"Parity symmetry enforces conditional Jarzynski equality in non-Hermitian hybrids","feed_subtitle":"The relation holds across the full SU(2) orbit of PT-APT Hamiltonians when transition probabilities obey parity exchange, confirmed at three","key_machinery":"The parity-exchange symmetry of the transition probabilities, demonstrated to remain invariant under SU(2) rotations of the hybrid PT-APT Hamiltonians.","core_discovery":"In a postselected no-quantum-jump framework, a conditional non-Hermitian Jarzynski equality holds when the transition probabilities obey a parity-exchange symmetry; this symmetry persists throughout the SU(2)-rotated orbit of hybrid PT-APT Hamiltonians. Relative to previous PT-focused results, the advance is the extension of the symmetry criterion to the broader hybrid family.","pith_inferences":["Similar symmetry criteria might be identifiable in higher-dimensional non-Hermitian systems that possess analogous parity relations.","Removing the postselection restriction would likely cause the equality to fail, indicating that experimental protocols must carefully enforce the no-jump condition.","The same symmetry-invariance technique could be applied to other fluctuation theorems in open quantum systems with balanced gain and loss."],"forward_implications":["The conditional equality extends from the isolated PT point to every member of the SU(2)-rotated hybrid family.","Work distributions measured at the three tested points (θ_k = 0, π/4, π/2) obey the equality for cyclic protocols with ΔF = 0.","Both geometric and algebraic arguments confirm that the parity-exchange symmetry is preserved along the entire orbit."],"fun_headline_variants":["Parity symmetry enforces Jarzynski equality across PT-APT hybrid family","Non-Hermitian Jarzynski equality holds under parity exchange in SU(2) orbit","Symmetry extends conditional Jarzynski to full PT-APT Hamiltonian family","SU(2) rotations preserve parity symmetry for non-Hermitian Jarzynski equality"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The derivation requires the dynamics to be restricted to the postselected no-quantum-jump framework.","fun_headline_variants_meta":{"raw":{"variants":["Parity symmetry enforces Jarzynski equality across PT-APT hybrid family","Non-Hermitian Jarzynski equality holds under parity exchange in SU(2) orbit","Symmetry extends conditional Jarzynski to full PT-APT Hamiltonian family","SU(2) rotations preserve parity symmetry for non-Hermitian Jarzynski equality"]},"model":"grok-4.3","cost_usd":0.006782,"raw_usage":{"total_tokens":3191,"prompt_tokens":741,"num_sources_used":0,"completion_tokens":84,"cost_in_usd_ticks":67824500,"prompt_tokens_details":{"text_tokens":741,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2366,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":741,"tokens_out":84,"duration_ms":19028,"temperature":1.0,"reasoning_tokens":2366,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-30T22:49:19.675387+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"An experiment that measures work distributions in a hybrid PT-APT system whose transition probabilities violate parity exchange yet still satisfy the conditional Jarzynski equality would falsify the necessity of the symmetry.","supporting_citations":[],"review_version":2}