{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:EG3BFQJJSOMS2XJVIK3D72B3FA","short_pith_number":"pith:EG3BFQJJ","canonical_record":{"source":{"id":"1408.5300","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-08-22T14:21:02Z","cross_cats_sorted":[],"title_canon_sha256":"1957020e5609a2fcabe7c5522b2c0e1041aa8fbc67a64703a226a162cc6476fe","abstract_canon_sha256":"bf1c177d100bf4bf9ee03503cb97a6a426586bc19af01b3383523039f1e679a2"},"schema_version":"1.0"},"canonical_sha256":"21b612c12993992d5d3542b63fe83b2833338f0d690ba78dc20722715b2012fb","source":{"kind":"arxiv","id":"1408.5300","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5300","created_at":"2026-05-18T01:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5300v1","created_at":"2026-05-18T01:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5300","created_at":"2026-05-18T01:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"EG3BFQJJSOMS","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EG3BFQJJSOMS2XJV","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EG3BFQJJ","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:EG3BFQJJSOMS2XJVIK3D72B3FA","target":"record","payload":{"canonical_record":{"source":{"id":"1408.5300","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-08-22T14:21:02Z","cross_cats_sorted":[],"title_canon_sha256":"1957020e5609a2fcabe7c5522b2c0e1041aa8fbc67a64703a226a162cc6476fe","abstract_canon_sha256":"bf1c177d100bf4bf9ee03503cb97a6a426586bc19af01b3383523039f1e679a2"},"schema_version":"1.0"},"canonical_sha256":"21b612c12993992d5d3542b63fe83b2833338f0d690ba78dc20722715b2012fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:42:13.890297Z","signature_b64":"fVWQY+zWLTnaX2MQBDL/U8/GmyU/AYiJusk7cSH20Qw06F64WXZIhFLlhYRyWr89B1lZ2Pz9pFs3jKxOy2sOBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21b612c12993992d5d3542b63fe83b2833338f0d690ba78dc20722715b2012fb","last_reissued_at":"2026-05-18T01:42:13.889704Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:42:13.889704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.5300","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W6MFgAzLQjaRpSrvws40Mow/yG/Cz7dOvGzbkkNz5yJRn30EGog3f2XmNqD9vC0hR6+NZC191fIhg1tP2p+iAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:37:21.428779Z"},"content_sha256":"7ff880764c7a62999a1920464aad04b6a3488c7df11355f4461b6a9cbc3fcd9b","schema_version":"1.0","event_id":"sha256:7ff880764c7a62999a1920464aad04b6a3488c7df11355f4461b6a9cbc3fcd9b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:EG3BFQJJSOMS2XJVIK3D72B3FA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Thermodynamics of N-dimensional quantum walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alejandro Romanelli, Franklin L. Marquezino, Raul Donangelo, Renato Portugal","submitted_at":"2014-08-22T14:21:02Z","abstract_excerpt":"The entanglement between the position and coin state of a $N$-dimensional quantum walker is shown to lead to a thermodynamic theory. The entropy, in this thermodynamics, is associated to the reduced density operator for the evolution of chirality, taking a partial trace over positions. From the asymptotic reduced density matrix it is possible to define thermodynamic quantities, such as the asymptotic entanglement entropy, temperature, Helmholz free energy, etc. We study in detail the case of a $2$-dimensional quantum walk, in the case of two different initial conditions: a non-separable coin-p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5300","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"myt3X3EZ+ges9XEx6jO3OJad1BcIOm3yWNd/8njsmlE//XxEANYMDe3EQkRqgT3/VUOfkdH7zeipPz9ugq+mBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:37:21.429462Z"},"content_sha256":"514258553219cc3a49cc1da9e0e2c33267dcbaca837caad2d96816cfac4abd65","schema_version":"1.0","event_id":"sha256:514258553219cc3a49cc1da9e0e2c33267dcbaca837caad2d96816cfac4abd65"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EG3BFQJJSOMS2XJVIK3D72B3FA/bundle.json","state_url":"https://pith.science/pith/EG3BFQJJSOMS2XJVIK3D72B3FA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EG3BFQJJSOMS2XJVIK3D72B3FA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T16:37:21Z","links":{"resolver":"https://pith.science/pith/EG3BFQJJSOMS2XJVIK3D72B3FA","bundle":"https://pith.science/pith/EG3BFQJJSOMS2XJVIK3D72B3FA/bundle.json","state":"https://pith.science/pith/EG3BFQJJSOMS2XJVIK3D72B3FA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EG3BFQJJSOMS2XJVIK3D72B3FA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EG3BFQJJSOMS2XJVIK3D72B3FA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"bf1c177d100bf4bf9ee03503cb97a6a426586bc19af01b3383523039f1e679a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-08-22T14:21:02Z","title_canon_sha256":"1957020e5609a2fcabe7c5522b2c0e1041aa8fbc67a64703a226a162cc6476fe"},"schema_version":"1.0","source":{"id":"1408.5300","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5300","created_at":"2026-05-18T01:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5300v1","created_at":"2026-05-18T01:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5300","created_at":"2026-05-18T01:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"EG3BFQJJSOMS","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EG3BFQJJSOMS2XJV","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EG3BFQJJ","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:514258553219cc3a49cc1da9e0e2c33267dcbaca837caad2d96816cfac4abd65","target":"graph","created_at":"2026-05-18T01:42:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The entanglement between the position and coin state of a $N$-dimensional quantum walker is shown to lead to a thermodynamic theory. The entropy, in this thermodynamics, is associated to the reduced density operator for the evolution of chirality, taking a partial trace over positions. From the asymptotic reduced density matrix it is possible to define thermodynamic quantities, such as the asymptotic entanglement entropy, temperature, Helmholz free energy, etc. We study in detail the case of a $2$-dimensional quantum walk, in the case of two different initial conditions: a non-separable coin-p","authors_text":"Alejandro Romanelli, Franklin L. Marquezino, Raul Donangelo, Renato Portugal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-08-22T14:21:02Z","title":"Thermodynamics of N-dimensional quantum walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5300","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7ff880764c7a62999a1920464aad04b6a3488c7df11355f4461b6a9cbc3fcd9b","target":"record","created_at":"2026-05-18T01:42:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bf1c177d100bf4bf9ee03503cb97a6a426586bc19af01b3383523039f1e679a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-08-22T14:21:02Z","title_canon_sha256":"1957020e5609a2fcabe7c5522b2c0e1041aa8fbc67a64703a226a162cc6476fe"},"schema_version":"1.0","source":{"id":"1408.5300","kind":"arxiv","version":1}},"canonical_sha256":"21b612c12993992d5d3542b63fe83b2833338f0d690ba78dc20722715b2012fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21b612c12993992d5d3542b63fe83b2833338f0d690ba78dc20722715b2012fb","first_computed_at":"2026-05-18T01:42:13.889704Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:42:13.889704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fVWQY+zWLTnaX2MQBDL/U8/GmyU/AYiJusk7cSH20Qw06F64WXZIhFLlhYRyWr89B1lZ2Pz9pFs3jKxOy2sOBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:42:13.890297Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.5300","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ff880764c7a62999a1920464aad04b6a3488c7df11355f4461b6a9cbc3fcd9b","sha256:514258553219cc3a49cc1da9e0e2c33267dcbaca837caad2d96816cfac4abd65"],"state_sha256":"d3e5382f92aea75ec20bdef8df18af1e006ac90dce0c8a9f64a829008c93c715"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jhbfbKFXjMJLCf2Dmq9xQJ/56zQTqzaMt0e/3S+EngNHEz6Gx9kKDf4Wz9Drv81tKTmCvvekpXZXdczzyfUkBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:37:21.433292Z","bundle_sha256":"0494d114de09629591639f33c291aef32453518ce543c0a1e83d8b9a9f6a939c"}}