What is claimed is:1. A method, comprising:receiving from a host application, an indication of a first minimum retention time in a cache comprising a first type of memory and a second type of memory for a first plurality of tracks, wherein the first minimum retention time is not indicated for a second plurality of tracks;based on the first minimum retention time, setting a second minimum retention time for the first plurality of tracks for the first type of memory and a third minimum retention time for the first plurality of tracks for the second type of memory; anddemoting a track of the first plurality of tracks from the first type of memory, in response to determining that the track is a least recently used (LRU) track in a LRU list of tracks in the first type of memory and the track has been in the first type of memory for a time that exceeds the second minimum retention time.2. The method of claim 1, wherein the first type of memory is a dynamic random access memory (DRAM) cache and the second type of memory is a storage class memory (SCM) cache, and wherein the second minimum retention time is a DRAM cache minimum retention time and the third minimum retention time is a SCM cache minimum retention time.3. The method of claim 2, the method further comprising:demoting, by a cache management application, a track of the first plurality of tracks from the SCM cache, in response to determining that the track is a least recently used (LRU) track in a LRU list of tracks in the SCM cache and the track has been in the SCM cache for a time that exceeds the SCM cache minimum retention time.4. The method of claim 2, wherein the indication of the first minimum retention time in cache comprises an individual minimum retention time for the DRAM cache and an individual minimum retention time for the SCM cache, wherein the DRAM cache minimum retention time is set to the individual minimum retention time for the DRAM cache, and wherein the SCM cache minimum retention time is set to the individual minimum retention time for the SCM cache.5. The method of claim 2, wherein the indication of the first minimum retention time in cache comprises an aggregate minimum retention time for the DRAM cache and the SCM cache, wherein the DRAM cache minimum retention time is set to a predetermined percentage of the aggregate minimum retention time, and wherein the SCM cache minimum retention time is set to a remaining percentage of the aggregate minimum retention time.6. The method of claim 2, wherein while promoting a track securing more than a predetermined number of hits from the SCM cache to the DRAM cache, unless a new first minimum retention time is provided for the track by the host application, a cache management application sets the DRAM cache minimum retention time to a difference of the SCM cache minimum retention time and the time the track has spent in the SCM cache prior to being promoted to the DRAM cache.7. The method of claim 2, wherein promoting a track from the DRAM cache to SCM cache comprises adding an unutilized time for the track in the DRAM cache to the SCM cache minimum retention time, wherein the DRAM cache has a lower latency and a lower storage capacity than the SCM cache, and wherein the DRAM cache and the SCM cache form a two-tier cache with the DRAM cache being a higher tier and the SCM cache being a lower tier, and wherein for the second plurality of tracks a cache management application does not set the DRAM cache minimum retention time and the SCM cache minimum retention time.8. A system, comprising:a memory; anda processor coupled to the memory, wherein the processor performs operations, the operations performed by the processor comprising:receiving from a host application, an indication of a first minimum retention time in a cache comprising a first type of memory and a second type of memory for a first plurality of tracks, wherein the first minimum retention time is not indicated for a second plurality of tracks;based on the first minimum retention time, setting a second minimum retention time for the first plurality of tracks for the first type of memory and a third minimum retention time for the first plurality of tracks for the second type of memory; anddemoting a track of the first plurality of tracks from the first type of memory, in response to determining that the track is a least recently used (LRU) track in a LRU list of tracks in the first type of memory and the track has been in the first type of memory for a time that exceeds the second minimum retention time.9. The system of claim 8, wherein the first type of memory is a dynamic random access memory (DRAM) cache and the second type of memory is a storage class memory (SCM) cache, and wherein the second minimum retention time is a DRAM cache minimum retention time and the third minimum retention time is a SCM cache minimum retention time.10. The system of claim 9, the operations further comprising:demoting, by a cache management application, a track of the first plurality of tracks from the SCM cache, in response to determining that the track is a least recently used (LRU) track in a LRU list of tracks in the SCM cache and the track has been in the SCM cache for a time that exceeds the SCM cache minimum retention time.11. The system of claim 9, wherein the indication of the first minimum retention time in cache comprises an individual minimum retention time for the DRAM cache and an individual minimum retention time for the SCM cache, wherein the DRAM cache minimum retention time is set to the individual minimum retention time for the DRAM cache, and wherein the SCM cache minimum retention time is set to the individual minimum retention time for the SCM cache.12. The system of claim 9, wherein the indication of the first minimum retention time in cache comprises an aggregate minimum retention time for the DRAM cache and the SCM cache, wherein the DRAM cache minimum retention time is set to a predetermined percentage of the aggregate minimum retention time, and wherein the SCM cache minimum retention time is set to a remaining percentage of the aggregate minimum retention time.13. The system of claim 9, wherein while promoting a track securing more than a predetermined number of hits from the SCM cache to the DRAM cache, unless a new first minimum retention time is provided for the track by the host application, a cache management application sets the DRAM cache minimum retention time to a difference of the SCM cache minimum retention time and the time the track has spent in the SCM cache prior to being promoted to the DRAM cache.14. The system of claim 9, wherein promoting a track from the DRAM cache to SCM cache comprises adding an unutilized time for the track in the DRAM cache to the SCM cache minimum retention time, wherein the DRAM cache has a lower latency and a lower storage capacity than the SCM cache, and wherein the DRAM cache and the SCM cache form a two-tier cache with the DRAM cache being a higher tier and the SCM cache being a lower tier, and wherein for the second plurality of tracks a cache management application does not set the DRAM cache minimum retention time and the SCM cache minimum retention time.15. A computer program product, the computer program product comprising a computer readable storage medium having computer readable program code embodied therewith, the computer readable program code configured to perform operations, the operations comprising:receiving from a host application, an indication of a first minimum retention time in a cache comprising a first type of memory and a second type of memory for a first plurality of tracks, wherein the first minimum retention time is not indicated for a second plurality of tracks;based on the first minimum retention time, setting a second minimum retention time for the first plurality of tracks for the first type of memory and a third minimum retention time for the first plurality of tracks for the second type of memory; anddemoting a track of the first plurality of tracks from the first type of memory, in response to determining that the track is a least recently used (LRU) track in a LRU list of tracks in the first type of memory and the track has been in the first type of memory for a time that exceeds the second minimum retention time.16. The computer program product of claim 15, wherein the first type of memory is a dynamic random access memory (DRAM) cache and the second type of memory is a storage class memory (SCM) cache, and wherein the second minimum retention time is a DRAM cache minimum retention time and the third minimum retention time is a SCM cache minimum retention time.17. The computer program product of claim 16, the operations further comprising:demoting, by a cache management application, a track of the first plurality of tracks from the SCM cache, in response to determining that the track is a least recently used (LRU) track in a LRU list of tracks in the SCM cache and the track has been in the SCM cache for a time that exceeds the SCM cache minimum retention time.18. The computer program product of claim 16, wherein the indication of the first minimum retention time in cache comprises an individual minimum retention time for the DRAM cache and an individual minimum retention time for the SCM cache, wherein the DRAM cache minimum retention time is set to the individual minimum retention time for the DRAM cache, and wherein the SCM cache minimum retention time is set to the individual minimum retention time for the SCM cache.19. The computer program product of claim 16, wherein the indication of the first minimum retention time in cache comprises an aggregate minimum retention time for the DRAM cache and the SCM cache, wherein the DRAM cache minimum retention time is set to a predetermined percentage of the aggregate minimum retention time, and wherein the SCM cache minimum retention time is set to a remaining percentage of the aggregate minimum retention time.20. The computer program product of claim 16, wherein while promoting a track securing more than a predetermined number of hits from the SCM cache to the DRAM cache, unless a new first minimum retention time is provided for the track by the host application, a cache management application sets the DRAM cache minimum retention time to a difference of the SCM cache minimum retention time and the time the track has spent in the SCM cache prior to being promoted to the DRAM cache.