demo, Sql Server - rextester

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--Sql Server 2014 Express Edition
--Batches are separated by 'go'

WITH TIMELINE AS (
    SELECT 1 AS Value UNION ALL
    SELECT 2 UNION ALL
    SELECT 3 UNION ALL
    SELECT 4 UNION ALL
    SELECT 5 UNION ALL
    SELECT 6 UNION ALL
    SELECT 7
),
PROD_ENTRY AS (
    SELECT '2017/09/25  01:25:00' AS entry_1,       1 AS entry_2,              'aaa' AS entry_3 UNION ALL
    SELECT '2017/09/25  01:26:00',       1,              'bbb' UNION ALL
    SELECT '2017/09/25  03:32:00',       2,              'ccc' UNION ALL
    SELECT '2017/09/25  04:15:00',       3,              'ddd' UNION ALL
    SELECT '2017/09/25  05:05:00',       5,              'eee' UNION ALL
    SELECT '2017/09/26  13:25:00',       7,              'fff'
)

SELECT
    new_value, entry_time, entry_2, entry_3
FROM
(
    SELECT
        t1.Value AS new_value,
        t2.entry_1 AS entry_time,
        t2.entry_2,
        t2.entry_3,
        ROW_NUMBER() OVER (PARTITION BY t1.Value ORDER BY t2.entry_1 DESC) rn
    FROM TIMELINE t1
    LEFT JOIN PROD_ENTRY t2
        ON t1.Value = t2.entry_2
) t
WHERE t.rn = 1
ORDER BY
    new_value;

View schema
Execution time: 0,02 sec, rows selected: 7, rows affected: 0, absolute service time: 0,16 sec