1. A computer-implemented method for carrying out an input/output (I/O) operation issued to a logical volume, the method comprising: receiving the I/O operation, wherein the I/O operation specifies a logical address that corresponds to an address tree associated with the logical volume; determining whether the address tree includes an entry associated with the logical address, wherein the entry stores physical address information that is associated with the logical address; and when the entry is not identified, and the I/O operation specifies a write request: issuing an allocation request to a physical device manager to allocate a number of blocks specified in the I/O operation, receiving, from the physical device manager, generated physical address information that specifies reserved storage space sized according to the number of blocks specified in the I/O operation, generating one or more entries within the address tree that is associated with the logical address, storing the generated physical address information in the one or more entries, translating the I/O operation into one or more write operations based on the generated physical address information, and forwarding the one or more write operations to the physical device manager to carry out the one or more write operations.